My title

Analysis of low-mass and high-mass systems after the common-envelope phase Analyse von Sternsystemen niedriger und hoher Masse nach der Common-Envelope Phase

Analysis of low-mass and high-mass systems after the common-envelope phase Analyse von Sternsystemen niedriger und hoher Masse nach der Common-Envelope Phase

Der Naturwissenschaftlichen Fakultät der Friedrich-Alexander-Universität Erlangen-N¨ urnberg zur Erlangung des Doktorgrades Dr. rer. nat. vorgelegt von

Veronika Katharina Schaffenroth aus Sulzbach-Rosenberg

Als Dissertation genehmigt von der Naturwissenschaftlichen Fakultät der Friedrich-Alexander-Universität Erlangen-N¨ urnberg

Tag der m¨ undlichen Pr¨ ufung: 17.07.2015

Vorsitzender des Promotionsorgans: Prof. Dr. Jörn Wilms Gutachter: Prof. Dr. Ulrich Heber und Prof. Dr. Norbert Przybilla Gutachter: Prof. Dr. Rolf-Peter Kudritzki

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Cover page: Illustrations of the common-envelope phase of two stars and the ejection of a runaway star out of the galaxy by Andreas Irrgang, and an illustration of planets orbiting a hot subdwarf star by Stephane Charpinet. Background: Solar spectrum, credit: N. A. Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF

Zusammenfassung Als enge Doppelsterne bezeichnet man zwei gravitativ gebundene Sterne mit so geringem Abstand, dass sie in ihrer Lebenszeit mindestens einmal wechselwirken. Dies geschieht meistens durch Massentransfer in der Roten Riesen Phase. Wenn beide Sterne ähnliche Masse besitzen, beginnt ein stabiler Massentransfer u ¨ber den Lagrange Punkt zwischen beiden Sternen auf den Begleiterstern, sobald der massereichere Stern sich zur Roten Riesen Phase hin entwickelt und dabei ausdehnt. Wenn der Massenunterschied in einem engen Doppelstern M1 /M2 > 1.5 u ¨berschreitet, kann der Begleiter jedoch nicht die gesamte transferierte Masse aufnehmen und es bildet sich eine gemeinsame H¨ ulle (Common Envelope) um beide Sterne. Dieses kurze Stadium wird “Common-Envelope Phase” genannt. Aufgrund von Reibung mit der H¨ ulle schrumpft der Abstand beider Sterne und die dabei frei werdende Orbitalenergie kann benutzt werden, um die H¨ ulle abzustoßen. Dabei entsteht ein sehr enges post Common-Envelope Doppelsternsystem (PCEB). Diese Phase ist aüßerst wichtig f¨ ur das Verständnis der Doppelsternentwicklung und dient der Erklärung einiger Phänomene von kosmologischer Bedeutung wie zum Beispiel die Supernovae vom Typ Ia. Trotz ihrer großen Bedeutung ist unser Verständnis daf¨ ur leider noch sehr begrenzt. Die Beobachtung von Doppelsternsystemen, in denen der Abstand beider Sterne im Bereich von einem Sonnenradius ist – viel kleiner als die typische Ausdehnung eines Roten Riesen – zeigt, dass diese Phase existieren muss. Jedoch sind die physikalischen Prozesse noch nicht verstanden. Im Moment wird diese Phase in der Modellierung nur parameterisiert. Die Modellparameter f¨ ur die Effizienz von Energie- und Drehimpulstransport sind jedoch noch immer unbekannt. Diese Arbeit beschäftigt sich mit der Analyse von Systemen mit geringer Masse nach der Common-Envelope Phase sowie einem einzigartigen, massereichen Stern, einem sogenannten Hyper-Runaway Stern, der ebenfalls durch eine Common-Envelope Ejektionsphase (CEE) gegangen sein muss. Die Systeme mit niedriger Masse, die hier untersucht wurden, bestehen aus einem heißen Subdwarf Primärstern mit einem Hauptreihenstern niedriger Masse oder einem braunen Zwerg als Begleiter. Heiße Subdwarfs vom Spektraltyp B (sdBs) sind Sterne, die sich in der Phase des Kern-Helium-Brennens befinden, jedoch fast ihre gesamte Wasserstoffh¨ ulle auf dem Roten Riesenast verloren haben. Da 50% der sdBs in engen Doppelsternen gefunden wurden, kann man ihre Entstehung am besten durch Doppelsternentwicklung erklären. Besonders enge Doppelsterne mit Perioden von Stunden, in denen das Massenverhältnis beider Komponten 5:1 beträgt, m¨ ussen eine CEE Phase durchlaufen haben. Ein anderer Erklärungsvorschlag ist, dass nicht nur massearme Hauptreihensterne sondern auch Planeten oder braune Zwerge f¨ ur die Entstehung des sdB verantwortlich sein könnten, wenn sie vom Stern auf dem Roten Riesenast “verschluckt” werden. Deshalb sind enge sdB Doppelsterne ideal, um den Einfluss von Planeten auf die Sternentwicklung zu untersuchen. Bedeckende Doppelsternsysteme bestehend aus sdB Sternen und massearmen, k¨ uhlen Begleitern (HW Virginis Systeme) sind besonders wichtig und interessant, da man in diesen die Inklination des Systems und damit auch die Massen und den Abstand beider Begleiter bestimmen kann. Diese Information ist essentiell, um die Common-Envelope Phase zu verstehen. Der erste Teil dieser Arbeit beschäftigt sich mit der Analyse und der Suche nach HW Virginis Systemen. Doppelsterne bestehend aus heißen sdB Sternen (mit Effektivtemperatur Teff ∼ 30 000 K) mit massearmen, k¨ uhlen Begleitern (Teff ∼ 3 000 K) zeigen charakteristische Lichtkurven, die sich durch den Reflexionseffekt auszeichnen. Dieser resultiert aus der großen Temper-

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aturdifferenz, die bewirkt, dass der k¨ uhle Begleiter auf der dem heißen Primärstern zugewandten Seite aufgeheizt wird. Je mehr von der aufgeheizten Seite des Begleiters sichtbar ist, desto größer ist seine Helligkeit, ähnlich wie bei den verschiedenen Mondphasen. Da eine Lichtkurve die Variation der Gesamthelligkeit darstellt, bewirkt die wechselnde Helligkeit des Begleiters eine sinusförmige Variation in der Lichtkurve. Aufgrund ihrer unverwechselbaren Lichtkurve wurden viele der HW Virginis Systeme in photometrischen Durchmusterungen gefunden, die Lichtkurven von einer großen Anzahl von Sternen beobachten. Mehrere interessante enge, bedeckende Doppelsterne, die auf diese Art entdeckt wurden, wurden in dieser Arbeit durch eine kombinierte spektroskopische und photometrische Analyse untersucht. Dies erhöht die Anzahl der untersuchten HW Virginis Systeme um 40% auf 17. Dies bietet genug Statistik, um Schl¨ usse u ¨ber die Massen- und Periodenverteilung der bedeckenden sdB PCEB Systeme zu ziehen und diese mit PCEB Systemen mit weißen Zwergen und k¨ uhlen, massearmen Begleitern, zu denen sich sdBs entwickeln werden, zu vergleichen. Unsere photometrische Untersuchung von spektroskopisch selektierten sdB Doppelsternen im MUCHFUSS (Massive Unseen Companion to Hot Faint Underluminous Stars from SDSS) Projekt mit Hilfe des Sloan Digital Sky Surveys (SDSS) erlaubte uns außerdem zum ersten Mal, den Anteil an Reflexionseffekt-Doppelsternen und substellareren Begleitern um sdB Sterne zu bestimmen. Deren Analyse zeigte, dass mehr als 3% der sdB Doppelsterne Braune Zwerg Begleiter besitzen. Dies zeigt, dass substellare Begleiter sehr wohl die Sternentwicklung beeinflussen können. Diese Doktorarbeit ist die Grundlage f¨ ur das EREBOS (Eclipsing Reflection Effect Binaries from the OGLE Survey) Projekt, das wir gerade begonnen haben. Dieses Projekt hat zum Ziel 36 im OGLE (Optical Gravitational Lensing Experiment) Survey neu entdeckte HW Virginis Systeme zu untersuchen und damit das Sample zu verdreifachen, um die Rolle von Planeten auf die Sternentwicklung besser zu untersuchen und die Common-Envelope Phase besser zu verstehen. Der zweite Teil dieser Doktorarbeit beschäftigt sich mit einem einzigartigen Runaway Stern. Als Runaway Sterne werden (massereiche) Sterne bezeichnet, die ihre Entstehungsregion mit hoher Geschwindigkeit verlassen (haben). Bei den im Galaktischen Halo in geringer Zahl auftretenden massereichen Sternen muss es sich um Runaway Sterne handeln, da dort aufgrund der geringen Dichte des interstellaren Mediums keine Sternentstehung stattfindet. Diese Sterne m¨ ussen in der Scheibe entstanden sein und binnen kurzer Zeit ausgeworfen worden sein. Um Runaway Sterne mit sehr hohen Geschwindigkeiten zu erklären, wurde das Standard-Auswurfszenario in einem Doppelstern von Przybilla et al. (2008) auf enge PCEB Systeme erweitert. Dabei entwickelt sich der deutlich massereichere Primärstern schnell, was zu einer gemeinsamen H¨ ulle aufgrund des instabilen Massentransfers f¨ uhrt. Nach der Common-Envelope Phase bleibt ein enges Doppelsternsystem zur¨ uck. Sobald der Primärstern in einer Kernkollapssupernova explodiert, kann sich der Begleiter mit nahezu der Orbitalgeschwindigkeit entfernen. Dabei kann die Atmosphäre des Begleiters Supernova-Auswurfmaterial akkretieren. Das bedeutet, dass solche Sterne sehr geeignet sind, um die Nukleosynthese während einer Kernkollapssupernova zu untersuchen. HD 271791 ist der einzig bekannte Runaway Stern dessen galaktische Ruhesystem-geschwindigkeit (750 ± 150km s−1 ) die Fluchtgeschwindigkeit der Galaxis u ¨bersteigt. Er wird daher als HyperRunaway Stern bezeichnet. Die bisherigen Studien zu diesem Stern durch Przybilla et al. (2008) haben eine Anreicherung der α−Prozess Elemente gezeigt. Dies weist auf die Akkretion von Supernova Auswurfmaterial hin. Da im normalen Supernova Szenario solch hohe Geschwindigkeiten nicht erreicht werden, wird ein sehr massereicher, jedoch kompakter Primärstern benötigt, höchstwahrscheinlich ein Wolf-Rayet-Stern, der entstehen sollte, wenn in der Common-Envelope Phase die H¨ ulle abgestoßen wird. Die theoretische Untersuchung dieses Systems durch Gvaramadze (2009) hat jedoch bezweifelt, dass es möglich ist durch eine Supernova den Runaway zu solchen Geschwindigkeiten zu beschleunigen. Die vorherige Untersuchung von HD 271791 wurde nur an optischen Spektren durchgef¨ uhrt, in denen nur wenige Elemente sichtbar sind. Weitere chemische Elemente können nur anhand von Ultraviolettspektren untersucht werden. Dazu wurden Beobachtungen mit dem Hubble

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Space Teleskop durchgef¨ uhrt. Das Ziel ist es die Nukleosynthese in einer Kernkollapssupernova näher zu untersuchen, indem die Modelle f¨ ur die Spektrumsyntheserechnungen f¨ ur das UV erweitert werden, um in diesem Wellenlängenbereich Elementhäufigkeiten zu bestimmen. In diesem Bereich ist ein Großteil der Linien der schwereren Elemente sichtbar. Vor allem sind dort auch Linien der Elemente zu sehen, die nur durch schnellen Neutroneneinfang (rProzess) produziert werden können. Dieser sollte in Kernkollapssupernovae stattfinden, da dort die notwendigen hohen Neutronenfl¨ usse auftreten. Die Spektrumsynthese wurde an vier hellen B Sternen mit verschiedenen Temperaturen von 17500-33000 K getestet, basierend auf Sternparametern, die im Optischen bestimmt wurden. Anschließend wurde HD 271791 mit einem Spektrum mit besserer Qualität im Optischen erneut untersucht, um genauere Sternparameter und Elementhäufigkeiten zu bestimmen. Es wurden auch einige Simulationen durchgef¨ uhrt, um zu bestimmen, welche Geschwindigkeiten unser Objekt im Supernova Szenario erreichen kann, was R¨ uckschl¨ usse auf das post Common-Envelope System zulässt. Basierend auf den stellaren Parametern, die im Optischen bestimmt wurden, konnten Elementhäufigkeiten f¨ ur Elemente bis zur Eisengruppe bestimmt werden. Diese Arbeit bietet nun die Grundlage f¨ ur die Bestimmung von Elementhäufigkeiten von B Sternen im UV. Es ist jetzt möglich Elementhäufigkeiten auch f¨ ur die Eisengruppe und Elemente dar¨ uber hinaus zu bestimmen. Damit sollte die genauere Untersuchung der Nukleosynthese in einer Kernkollapssupernova, insbesondere der r-Prozess Elemente, in naher Zukunft möglich sein.

Abstract Close binaries are two gravitationally bound stars, which orbit each other with a sufficiently small separation so that they interact with each other at least once in their lifetime. This happens mostly by mass transfer in the red giant phase. If both stars have similar masses, a stable mass transfer via the Lagrange points between them will be initiated as soon as the more massive star evolves towards the red giant branch and is expanding. In close binaries with sufficient mass difference (M1 /M2 > 1.5) the companion cannot accrete all mass transfered and a common envelope around both stars is formed. Because of friction in the envelope the separation of both stars shrinks and the free orbital energy can be used to eject the envelope. The outcome is a very close binary, a post common-envelope binary system (PCEB). This phase is highly important for the understanding of binary evolution and as well as for the explanation of for example supernovae of type Ia, which are of cosmological significance. Despite this fact, our understanding of this immensely important phase is quite limited. The observation of binaries with separations of the order of a solar radius – much smaller than the typical radius of a red giant of hundreds of solar radii – shows that the common-envelop phase has to exist, but the physical processes are only qualitatively understood. The description of this phase is only parametrized in binary stellar evolution models at the moment. The model parameters for the efficiency of the transport of the energy and angular momentum, however, are still unknown. This thesis covers the analysis of low-mass systems as well as the analysis of a unique, massive star, a so-called hyper-runaway star, which has to have undergone a common-envelope ejection phase. The low-mass systems investigated here are very close binaries consisting of a hot subdwarf primary star and a low-mass main-sequence or brown dwarf companion. Hot subdwarf stars of spectral type B (sdB) are core-helium burning stars on the extreme horizontal branch, which lost almost their entire hydrogen envelope on the tip of the red giant branch. As about 50% of the sdBs are found in close binary systems, the best explanation for their formation is binary evolution. In particular close sdB binaries with periods of hours and with a mass ratio of 5:1 can only be explained by a previous common-envelope phase. It was also suggested that not only low-mass stars but also planets or brown dwarfs could be responsible for the mass loss, when they are engulfed in the envelope of the star. Therefore, close sdB binaries with low-mass companions are ideal to study the influence of planets on stellar evolution. Of those, eclipsing (HW Virginis systems) are in particular important, as the inclination can be determined and, hence, the masses and separation can be derived, which are essential for the understanding of the common-envelope phase. The topic of the first part of this thesis is the analysis and the search for common-envelope systems. Binaries consisting of hot subdwarf stars (with effective temperature Teff = 30 000 K) with low-mass, cool companions (Teff = 3 000 K) have characteristic lightcurves showing the reflection effect. This effect results from the large temperature difference between the two objects. Consequently, the cool companion is heated up on one side by the close hot primary star. The more of the heated side of the companion is visible, the higher is its luminosity similar to the different moon phases. As a lightcurve represents the time evolution of the combined luminosity of both components, the varying flux of the companion causes a sinusoidal variation in the lightcurve. Many of the HW Virginis systems have been found in photometric surveys, which observe lightcurves of a large number of stars, due to the easily recognizable lightcurve. Several eclipsing sdB binaries, which have been found in this way, were investigated in this

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thesis by a combined photometric and spectroscopic analysis. This increased the number of analyzed HW Virginis systems by 40 % to 17 providing a sufficiently large sample to draw first conclusions about their mass and period distribution and a comparison to PCEBs with white dwarf primaries, which are the successors of the sdB binaries. Our photometric investigation of spectroscopically selected sdB binaries from the Sloan Digital Sky Survey allowed us to determine the fraction of reflection effect binaries and substellar objects around sdB stars for the first time. The analysis showed that more than 3% of the sdB binaries have substellar companions. This shows that substellar companions can indeed influence stellar evolution. This work is the basis for the EREBOS (Eclipsing Binaries from the OGLE Survey) that we just started. This project aims at studying 36 HW Virginis systems recently discovered by the OGLE (Optical Gravitational Lensing Experiment) survey in order to further investigate the role of planets on stellar evolution and develop a better understanding of the common-envelope phase. The topic of the second part of this thesis is a unique runaway star. Runaway stars are (massive) stars that are currently leaving or already have left their birth-place with high velocity. The massive stars found in low numbers in the halo have to be runaway stars, as no star formation occurs there because of the low density of the interstellar medium. Those stars have to be formed in the Galactic disk and be ejected shortly afterwards. Przybilla et al. (2008) developed one ejection scenario: a supernova in a close PCEB system. The much more massive primary is evolving very fast and a common envelope around both stars is formed due to unstable mass transfer. The result is a massive binary in a very short orbit. When the more massive star explodes in a core-collapse supernova, the companion may be released nearly at its orbital velocity. The atmosphere of the runaway star can be polluted with the supernova ejecta in this process. Therefore, such kind of stars are ideally suited to study nucleosynthesis in a core collapse supernova. HD 271791 is the only known runaway star, whose galactic restframe velocity (740±150 km s−1 ) exceeds the escape velocity of the Galaxy. Hence, it is called a hyper-runaway star. A prior investigation of this star by Przybilla et al. (2008) has shown an enhancement of the α−process elements. This indicates the capture of supernova ejecta. As such high space velocities are not reached by the runaway stars in classical binary supernova ejection scenarios, a very massive but compact primary, probably of Wolf-Rayet type, is required, which is expected to be formed by ejecting the envelope in a common-envelope phase. A later theoretical investigation by Gvaramadze (2009) of this system put the acceleration scenario in question, finding it unlikely to accelerate a star with this properties to such high velocities. The first quantitative analysis of the star was based on optical spectra, which allowed abundances of only a small number of elements to be determined. More chemical elements can only be investigated with the help of ultraviolet spectra. Therefore, Hubble Space Telescope observations were obtained. The goal of this project is to further investigate nucleosynthesis in a core-collapse supernova. Hence, the spectrum synthesis computations were extended to the UV to facilitate abundance determinations in this spectral region, where many chemical species produce a dense forest of spectral lines. In particular, also the lines of elements that can only be produced by rapid neutron capture (r process) are visible there. They are suggested to be synthesized in core-collapse supernovae, as high neutron fluxes are available there. Hence, it could provide evidence for the r process taking place in core-collapse supernovae, if the r-process elements were found to be enhanced. The spectrum synthesis was tested by the abundance determination of four bright B stars with different temperatures from 17500 − 33000 K based on the stellar parameters determined from the analysis of the optical spectra. Afterwards, we re-investigated HD 271791 based on higher quality optical spectra to determine the stellar parameters and abundances with higher accuracy. We also performed some simulations to re-investigate the velocities a star, which has the properties of HD 271791, can reach in the supernova scenario. Based on the parameters from the optical analysis, our spectrum synthesis was used to derive abundances of HD 271791 for elements until the iron group in a second step.

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In summary, this work establishes the basis for comprehensive abundance determinations of B stars in the UV in the future, comprising iron-group elements and many heavier chemical species. This will ultimately facilitate to investigate nucleosynthesis in a core-collapse supernova in great detail by this novel approach.

Contents Zusammenfassung

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1. Introduction 2. Stellar evolution and nucleosynthesis 2.1. Stellar evolution . . . . . . . . . . . . . . 2.1.1. Stellar structure . . . . . . . . . . 2.1.2. Star formation . . . . . . . . . . 2.1.3. Main sequence . . . . . . . . . . . 2.1.4. Evolution after the main sequence 2.1.5. Evolution of massive stars . . . . 2.2. Nucleosynthesis beyond the iron peak . . 2.2.1. Slow neutron capture process . . 2.2.2. Rapid neutron capture process . . 2.3. Massive binary evolution . . . . . . . . .

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3. Hot 3.1. 3.2. 3.3.

subdwarf stars General properties . . . . . . . . . . . . . . . . . . . Formation scenarios . . . . . . . . . . . . . . . . . . . Hot subdwarfs in (eclipsing) binaries . . . . . . . . . 3.3.1. Hot subdwarf binaries with composite spectra 3.3.2. Hot subdwarfs in close binaries . . . . . . . . 3.3.3. Eclipsing sdB binaries - HW Virginis systems 3.4. Subdwarfs and substellar companions . . . . . . . . . 3.5. Pulsating hot subdwarfs and asteroseismology . . . .

4. Runaway stars 4.1. Binary-supernova scenario (BSS) . . . . . . . . 4.2. Dynamical interaction scenario (DES) . . . . . . 4.3. Hills mechanism . . . . . . . . . . . . . . . . . . 4.4. Importance of the different formation scenarios?

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5. Model Atmosphere Analysis & Spectral Line Formation 5.1. Model Atmospheres . . . . . . . . . . . . . . . . . . . 5.1.1. LTE vs. NLTE . . . . . . . . . . . . . . . . . 5.1.2. Line blanketing . . . . . . . . . . . . . . . . . 5.2. Radiative transfer . . . . . . . . . . . . . . . . . . . . 5.2.1. Radiative transfer equation . . . . . . . . . . 5.2.2. Properties of the radiation field . . . . . . . . 5.2.3. Methods to solve the transfer equation . . . . 5.3. Spectral line formation . . . . . . . . . . . . . . . . .

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6. Analysis methods 6.1. Analysis of (eclipsing) binaries . . . . . . . . . . . 6.1.1. Lightcurve analysis . . . . . . . . . . . . . 6.1.2. Time dependent spectroscopy . . . . . . . 6.1.3. Atmospheric parameters . . . . . . . . . . 6.2. Quantitative spectral analysis . . . . . . . . . . . 6.2.1. Fundamental parameters and abundances . 6.2.2. Mass, age and radius of the star . . . . . . 6.2.3. Distances . . . . . . . . . . . . . . . . . . 6.3. Stellar kinematics . . . . . . . . . . . . . . . . . .

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7. Analysis of hot subdwarfs with cool companions 7.1. The MUCHFUSS project . . . . . . . . . . . . . . . . . . . . . . . 7.1.1. Target selection . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2. Light variations and their observations with BUSCA . . . 7.2. Eclipse time variations in J0820 . . . . . . . . . . . . . . . . . . . 7.3. J1920 – A new typical HW Virginis system . . . . . . . . . . . . . 7.4. J1622 – A subdwarf B star with brown dwarf companion . . . . . 7.4.1. Observations . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2. Spectroscopic analysis . . . . . . . . . . . . . . . . . . . . 7.4.3. Photometric analysis . . . . . . . . . . . . . . . . . . . . . 7.4.4. The brown dwarf nature of the companion . . . . . . . . . 7.4.5. Synchronisation . . . . . . . . . . . . . . . . . . . . . . . . 7.4.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5. Two candidate BD companions around core He-burning objects . 7.5.1. Time-resolved spectroscopy and orbital parameters . . . . 7.5.2. Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.3. Brown dwarf nature of the unseen companions . . . . . . . 7.5.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6. An eclipsing binary with a pulsating sdB and a BD companion . . 7.6.1. Observations . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.2. Spectroscopic analysis . . . . . . . . . . . . . . . . . . . . 7.6.3. Photometric analysis . . . . . . . . . . . . . . . . . . . . . 7.6.4. The brown dwarf nature of the companion . . . . . . . . . 7.6.5. Summary and conclusions . . . . . . . . . . . . . . . . . . 7.7. OGLE-GD-ECL-08577 – The longest period HW Virginis system . 7.7.1. Observations . . . . . . . . . . . . . . . . . . . . . . . . . 7.7.2. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8. Photometric follow-up of the MUCHFUSS project . . . . . . . . . 7.8.1. Selection effects . . . . . . . . . . . . . . . . . . . . . . . . 7.8.2. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9. Statistics of hot subdwarfs with cool companions . . . . . . . . .

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73 73 73 74 77 80 82 82 83 84 86 87 91 93 93 94 98 99 101 101 103 106 109 111 115 115 117 123 128 129 131

8. Spectrum Synthesis in the UV 8.1. Hybrid LTE/NLTE approach . . . . . . . . . 8.2. Calculation of oscillator strengths . . . . . . . 8.2.1. Experimental measurement of oscillator 8.2.2. R-matrix method . . . . . . . . . . . . 8.2.3. Cowan code . . . . . . . . . . . . . . . 8.3. Atomic Data . . . . . . . . . . . . . . . . . . . 8.4. Tests . . . . . . . . . . . . . . . . . . . . . . .

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XIII

Contents

8.5. Spectral energy distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9. Spectroscopic analysis of four bright B stars in the UV 147 9.1. SEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 9.2. Abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 10.The extreme runaway HD 271791 10.1. Analysis of the optical spectrum . . . . . . . . . . . . . . . . . . . . . . . . 10.1.1. Correction of the O3 -Huggins Bands . . . . . . . . . . . . . . . . . 10.1.2. Fundamental parameters and abundances from the optical spectrum 10.2. Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3. Analysis in the UV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4. The supernova scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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155 155 156 158 160 164 165

11.Future work 167 11.1. Eclipsing hot subdwarf binaries – The EREBOS project . . . . . . . . . . . . . . 167 11.2. Spectrum synthesis in the UV and runaway stars . . . . . . . . . . . . . . . . . 168 Appendix A. Orbital parameters for known post common-envelope systems B. Atomic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Line distribution of different elements . . . . . . . . . . . . . . D. UV spectrum of ι Her . . . . . . . . . . . . . . . . . . . . . . E. UV spectrum of HD 271791 . . . . . . . . . . . . . . . . . . .

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XV XV XIX XXIII XC CXVI

Bibliography

CXXXI

Acknowledgements

CXLIII

1. Introduction The main goal of astrophysics is to develop a comprehensive understanding of the universe and our place in it. We are living in the Milky Way, which is one of the uncountable number of galaxies that are populating the universe. Each galaxy is composed of billions of stars that are gravitationally bound. In order to understand the evolution of galaxies, it is essential to know how stars evolve, as they are the main drivers of galactic evolution. In particular massive stars are highly important sources of heavy elements, the so-called metals, which they release by the action of stellar winds and, at the end of their lifetime, in supernovae. This enriches the interstellar medium out of which new stars are formed. However, most stars are not born single. The multiplicity fraction is depending strongly on the mass, as shown in Fig. 1.1. In particular stars with higher masses are almost all born in binaries (Sana et al. 2012). Hence, stellar evolution cannot be understood without investigating binary evolution. Two different types of binaries exist. The wide binaries do only interact gravitationally. They do not influence the evolution of their companion and can therefore be treated as two single stars. On the other hand, also close binaries exist, which are defined as binaries which are interacting with each other at some point in their lifetime, in particular during the giant phase. This interaction takes place mostly via mass transfer, which is influencing the evolution of both donor and gainer star in a decisive way. Very close binaries with large differences in their masses are experiencing a so-called commonenvelope phase. Common-envelope ejection (CEE) is the name of a short phase in the life of a close binary star during which both companions orbit inside a single, shared envelope. Common-envelope evolution is believed to be a vital process for the understanding of very close binary stars, which have separation smaller than the radius of a red giant star. Such binaries are essential for the explanation of some highly important phenomena, such as Type Ia supernovae or double neutron stars, which are the most important cosmological standard candles and primary targets for the direct detection of gravitational wave emission, respectively. Binary systems with separations smaller than the radius of the red giant, which can only be explained by CEE, are found in large numbers. Yet, the theoretical understanding of this very important phase is still limited. The current knowledge is summarized by Ivanova et al. (2013). Hydrodynamic simulations of the common-envelope phase still struggle to explain the removal of the envelope (see Fig. 1.2 for an example), however the observed post common-envelope systems discovered prove that this phenomenon occurs. The understanding is that, when the more massive star consumes its hydrogen in the core and evolves to a red giant, an unstable mass transfer is initiated in binaries with large mass difference. The consequence is a commonenvelope around both stars. Friction in the envelope leads to shrinking of the orbit. The released orbital energy is somehow transferred to the envelope and leads to its ejection. Another viable outcome could be the merger of both stars. However, the physical processes are still not yet fully understood. In the absence of a complete physical explanation, this phase is treated in a simplified way using free parameters, which are tuned to match the observations, or values are assumed to facilitate predictions. It is assumed that the binding energy Ebind is equal to the difference in

1

CHAPTER 1. INTRODUCTION

2

VLM

M

K G

A

early B

O

MF, CF

1.5

1.0

0.5

0.0 0.1

1.0 Stellar Mass (MO•)

10.0

Figure 1.1.: Dependency of the companion frequency (CF = average number of companions per observing target; red squares) and of the multiplicity frequency (MF; blue triangles) as a function of primary mass for main-sequence stars and very low-mass (VLM) objects in the field. The horizontal error bars represent the approximate mass range for each population. For B and O stars, only companions down to q ≈ 0.1 are included and only lower limits for the multiple system fraction (adopted from Duchêne & Kraus 2013).

the orbital energy ∆Eorbb : Ebind

m1 m1,env Gm1 m2 Gm1,c m2 =G = ∆Eorbb = αCE − + λR1 2ai 2af

(1.1)

where λ is a parameter to allow for differences in the envelope structure, ai and af is the initial and final binary separation, G = 6.67384 · 10−11 m3 kg−1 s−2 is the gravitational constant, m1 , m1,c and m1,env are the mass of the primary star and the mass of its core and envelope, R1 is the radius of the primary star, and m2 is the mass of the companion. As not all available orbital energy can be used to eject the envelope the common-envelope efficiency αCE is introduced, which gives the fraction of usable orbital energy. Since, CEE is central for the understanding of many types of different observed binary systems, it is uncomfortable that no physically robust explanation has been found for the process to date. Common-envelope evolution is one of the most important unsolved problems in stellar evolution, and is of critical importance for the understanding of binary evolution. As this phase is only short lived it is very difficult to discover systems that are currently in this phase. However, the investigation of different post common-envelope binary (PCEB) systems can help to understand this important phase and hopefully solve its mystery. Particular of importance are eclipsing PCEB systems as they allow the determination of the masses and separations of the companions. Most studies undertaken until now with eclipsing PCEBs use the αCE -formalism and aim to calibrate the existing parametrization (e.g., Zorotovic et al. 2010). On the other hand, the hydrodynamic simulations make several predictions of the characteristics of the PCEBs, as, e.g, a small eccentricity is expected. These predictions can be tested by observed PCEBs. In this work we investigate post common-envelope systems originating from low-mass binaries as well as one high-mass star thought to be the remnant of a disrupted PCEB system. The properties and evolution of these systems differ significantly. The low-mass binaries investigated in this thesis are PCEBs consisting of hot subdwarf stars of spectral type B (sdB) and low-mass main sequence or brown dwarf companions.

3

Figure 1.2.: Numerical simulation of a common envelope event with a 0.88 M giant and a 0.6 M main-sequence (MS) star likely leading to the formation of a close binary (Ivanova et al. 2013) in the orbital plane (left panel) and the perpendicular plan (right panel).

CHAPTER 1. INTRODUCTION

4

This class of systems is called HW Virginis systems after the prototype, when eclipsing. SdB stars are helium-burning cores that lost almost all their hydrogen envelope on the red giant branch (RGB). As about half of this systems are found in close binaries, binary evolution is considered to be the best explanation for the high mass loss on the RGB. In particular the eclipsing sdB binaries with periods of 0.065 to 0.5 d can only be explained by a previous common-envelope phase. This implies that binary evolution and common-envelope evolution is playing a highly important role in the formation of sdB stars. As the radii of both components in these binaries are of similar size (∼ 0.1 − 0.2 R ), they are suited very well to investigate the CEE due to the high probability of being eclipsing. These allows to determine the inclination and, hence, the separation of the system and the masses of both components, which is necessary to understand the previous CEE. Furthermore, this work investigates the massive runaway star HD 271791 in the Galactic halo, which shows unusual properties. Because of its large distance to the Galactic plane HD 271791 was regarded a runaway B star. HD 271791 attracted attention because of its very high radial velocity of 442 km s−1 (Kilkenny & Muller 1989). Heber et al. (2008) investigated this star by using high-resolution, high-S/N spectra. They derived that the star is a massive B giant. From the proper motions of the star they get a Galactic rest-frame velocity of 530 − 920 km s−1 , which implies that this star is unbound to the Galaxy. The birth-place was discovered to be on the outskirts of the Galactic disc with a Galactocentric distance of & 15 kpc. Przybilla et al. (2008) performed a quantitative analysis of the star to get some hints on the ejection scenario. One theory for its origin is that it was member of a close post common-envelope system. The more massive companion exploded in a supernova, which lead to the ejection of the runaway. The runaway is, moreover, hit by the ejecta of the supernova, which polluted its atmosphere. An accurate determination of the surface composition confirmed the low [Fe/H] expected for a star born in the outer Galactic rim. The detected α−enhancement points towards an extreme case of the binary-supernova runaway scenario. Therefore, this star promises to shed light on nucleosynthesis that is expected to take place in a core-collapse supernova. In particular, it may facilitate an empirical verification of the occurrence of the r-process in core-collapse supernovae. As it turned out complicated to derive detailed abundance information from direct observations of core-collapse supernovae, and the observation of nebula spectra provides only abundance data for few elements. At the moment observational constraints on SN nucleosynthesis are only obtained by indirect methods, like the secondary stars in low-mass X-ray binaries or the abundance patterns of metal-poor halo stars. Our approach is adding a new promising method to investigate this. In order to shed further light on the topic, we re-investigate in this thesis this highly interesting star by using higher S/N optical spectra taken with ESO-VLT/UVES, as well as UV spectra taken with HST/STIS and COS to investigate the abundances of the heavier elements. The first part of this thesis concentrates on the discussion of the (astro)physical background. To understand the formation of an sdB and a runaway star it is necessary to understand the stellar evolution of low-mass as well as high-mass stars. Chapter 2 summarizes the basics of stellar evolution, with a particular focus on nucleosynthetic processes taking place in stars and core-collapse supernovae, information which is highly important for the understanding of the analysis of the runaway star. Chapter 3 and 4 gives some details about the current knowledge of hot subdwarf stars as well as massive runaway stars. Model atmospheres and the calculation of synthetic spectra are discussed in Chapter 5 and the analysis methods employed in this work in Chapter 6. After introducing all the basics, the results of the analysis of the hot subdwarf stars with cool low mass companions is then presented in Chapter 7. As the majority of spectral lines in hot massive stars is located in the UV, spectral synthesis at these wavelengths had to be implemented for the present project, which is discussed in Chapter 8. Tests and first applications to a sample of four bright, sharp-lined stars for a range of effective temperatures are presented in Chapter 9. The runaway star HD 271791 is investigated in Chapter 10, focusing

5

on an analysis of its optical and UV spectrum and of its kinematics to determine its birthplace in the Galactic disk. Finally an outlook is given in Chapter 11.

2. Stellar evolution and nucleosynthesis To understand the low-mass sdB PCEB systems and the massive runaway star investigated in this thesis it is necessary to get an idea about the stellar evolution of low-mass as well as highmass stars. As the stellar evolution differs greatly with mass will introduce stellar evolution in some detail. This will be followed by an introduction to the nucleosynthetic processes, which is essential for the understanding of the analysis of the post-supernova companion. As the stellar evolution in binaries differs from the single star evolution, I will discuss this also shortly at the end of the chapter. This chapter is mostly based on the textbooks of Kippenhahn & Weigert (1994), Iliadis (2007), Clayton (1983), Carroll & Ostlie (2007), and lecture notes by O.R. Pols1 .

2.1. Stellar evolution 2.1.1. Stellar structure To understand stellar evolution and the calculation of stellar evolution tracks, it is important to first learn about the principle laws used to calculate the stellar structure. For simplicity some assumptions were adopted: no rotation, no magnetic fields, no mass loss, spherical symmetry, no companion. The conditions in the interior of a star are described completely by a set of four differential equations for the mass M , the density ρ, the luminosity L, and the pressure P . These equations representing the fundamental conservation laws: • mass conservation dMr = 4πρ(r)r2 → M = dr

ZR

4πρ(r)r2 dr

(2.1a)

0

thereby is Mr the mass within the radius r and R the stellar radius • hydrostatic equilibrium: momentum conservation dFpres + dFgrav = dP (r)dA − G

dP (r) Mr dm Mr ρ(r) = 0 −→ , = −G 2 r dr r2

(2.1b)

where dFpres is the pressure force, which acts on the area dA of an small mass element dm and dFgrav the gravitational force, which acts on this mass element. • energy conservation dL(r) = 4πρ(r)r2 , = n + g − ν dr

(2.1c)

thereby is ν the energy carried away by neutrinos, n the energy production due to nuclear fusion and g = −T dS the gravothermal energy. S is the entropy and T the temperature, dt and this means that energy also can be absorbed and transferred to heat dQ = T dS. 1

http://www.astro.uni-bonn.de/~nlanger/siu_web/teach_sse.html

7

CHAPTER 2. STELLAR EVOLUTION AND NUCLEOSYNTHESIS

8

Figure 2.1.: Illustration of the test of stability of the surrounding layer (s) by lifting a test element (e) (Kippenhahn & Weigert 1994)

• energy transport dT (r) 3 κν L(r) dT (r) T (r) GMr ρ(r) =− (radiative) or =− ∇ (convective) (2.1d) 3 2 dr 4ac T 4πr dr P (r) r2 ln T thereby is ∇ = dd ln and κν (the Rosseland opacity) the frequency dependent absorption P coefficient, c the speed of light and a = 7.57 · 10−15 erg cm−3 K−4 the radiation-density constant. There exists also energy transport by conduction, which plays only a minor role in normal stars, but is important for example in white dwarfs. To discriminate which kind of energy transport is dominant the Schwarzschild criterion is used. If κ or L(r) is large, the temperature gradient becomes large. However, there exists an upper limit for the possible temperature gradient inside stars - if it is exceeded, instability of the gas sets in. Therefore, energy cannot be transported by radiation alone any more. This instability leads to cyclic macroscopic motions of the gas, known as convection. Figure 2.1 illustrates the test used by Schwarzschild to determine the conditions for stability against convection. If the density of the element (e) is smaller than the density of the surrounding layer (s), the test element is able to rise and convection is initiated. Hence, the stability criterion is ∂ρ ∂ρ − > 0 → ∇rad < ∇ad ≈ ∇ (Schwarzschild criterion) dr e dr s

From the stability criterion together with the equation of state (pV = nkT , for an ideal gas) the Schwarzschild criterion can be derived in a more practical way by using tempera γ ln T ture gradients. Therefore, convection is possible, if ∇rad > ∇ad , ∇ad = dd ln = γ−1 P S=const (γ is the adiabatic coefficient, for an ideal gas: γ = 53 ) means the temperature gradient for an adiabatic expansion (no transfer of energy as heat) and ∇rad can be calculated by κν L(r)P dr 3 ∇rad = PT dT = 16πacG . dr dP mT 4 • Additionally there exists a fifth differential equation for the changes of the chemical composition with time " # X ∂Xi mi X = rji − rik , i = 1...I (2.1e) ∂t ρ j k

9

2.1. STELLAR EVOLUTION

thereby is Xi the mass fraction of the element i and rij the reaction rate for a transformation from element i in j. Each element i is produced by the reaction j → i and destroyed by the reaction i → j. These five differential equations can only be solved by assuming boundary conditions. Those are typically the central conditions: m(0) = 0, L(0) = 0 and the surface conditions: m(R) → M, L(R) → L The effective temperature Teff , which is defined by the Stefan-Boltzmann law: L = 4πR2 σTeff 4

(2.2)

with σ = 5.670373·10−8 W m−2 K−4 the Stefan-Boltzmann constant, is equal to the temperature at the photosphere Tr=R . Also (r), ρ(r), κ, γ, T (r), S, P (ρ, T ) have to be known to calculate the stellar structure. Based on the stellar structure it is possible to derive the stellar evolution, which is a time sequence of stellar structure calculations for modified chemical composition. 2.1.2. Star formation Stars form out of interstellar matter. A cloud of compressible gas can become gravitational unstable and collapse. To describe the condition when a gas cloud becomes unstable, the Jeans criterion is used. If gravity overcomes the gas pressure, the gas cloud becomes unstable. Only a small perturbation is required to initiate the gas cloud collapse. For the description of stars the Virial theorem (Ekin + 2Egrav = 0; Ekin is the kinetic energy and Egrav is the gravitational energy), known from statistical physics for a system in hydrostatic equilibrium, is also highly important. Using it we can derive the minimum mass needed to destabilize a gas cloud, called 1/2 5/2 3 Jeans mass MJ . For the spherical case we derive MJ > 4πρ · 5kT . The time-scale τ Gµ for such a collapse is τ ≈ (Gρ)−1/2 , the free-fall time. For typical values we get a Jeans mass of about MJ = 105 M , much larger than the stellar masses. The cloud fragments during the collapse into smaller clumps, which form the protostars. When the gas cloud is contracting, the temperature and the pressure in the core is increasing. Therefore, the collapse stops first in the core, where a state close to hydrostatic equilibrium is reached. However, surrounding mass is still accreted until the temperature and pressure is high enough to fuse hydrogen in the core. The radiation pressure resulting from the fusion processes prevents then the newly formed star from accreting additional mass. After some relaxation time a stable state is reached. The star has reached the main sequence. Massive stars can, in contrast to low-mass stars, only be formed in clusters or associations resulting from the collapse of giant molecular clouds. 2.1.3. Main sequence In the main-sequence phase the energy losses from a star’s surface are compensated by the energy production of hydrogen burning. These reactions release nuclear binding energy by converting hydrogen into helium. The evolution timescales differ by orders of magnitude with the stellar mass. As hydrogen is by far the most abundant element, the time spend on the main sequence is most of the lifetime of the star. It depends on the amount of nuclear fuel and the energy consumption (it can be approximated by τ ∝ M/L). This assumption is confirmed by stellar evolutionary tracks, which show that stars at the lower end of the main sequence (MS) with low masses and low luminosities live for billions of years while massive, early-type stars with high luminosities end their life after a few hundred million years or less.


10

Figure 2.2.: Comparison of the energy rate of the CNO1 cycle and the pp1 chain at different temperatures (http://www.nscl.msu.edu/~kontos/cnocycle.html) Hydrogen burning

Two different processes can occur during hydrogen-burning. For low-mass stars the pp-chains are the dominant reactions due to the lower core temperatures (see Fig. 2.2). The first two reactions are the same for each chain: p(p, e+ ν)d (d= 2H) and d(p, γ) 3He. The three pp-chains are displayed in Fig. 2.3. In the pp1 chain we get 4He from 3He( 3He, 2p) 4He. If the temperature is high enough and the abundance of 3He is high enough, also the pp2 and pp3 chain become possible, as the reaction 3He(α, γ) 7Be becomes dominant. As low-mass stars 0.35 . M . 1M have radiative cores, no mixing takes place and the hydrogen burning stops as soon as the hydrogen concentration in the core gets too low. Even lower mass stars are fully convective and will contract directly into white dwarfs after the hydrogen is exhausted. For more massive stars the CNO cycles are the dominant reactions to produce helium. However, that is only possible, if also heavier nuclides like C, N and O exist in the star, i.e. in all except the very first ones. C, N and O function only as catalysts for the transformation of hydrogen to helium. However, the cycles will change the abundances of the individual heavy nuclei. The reactions of the CNO cycles are displayed in Fig. 2.4. The dominant cycle is the CNO1 cycle. The bottle-neck in this cycle is the 14N(p, γ) 15O reaction, as this is the slowest process for temperatures below T < 0.1 GK. The net effect of the CNO1 cycle is, therefore, the conversion of carbon and nitrogen seed nuclei to 14N, which becomes by far the most abundant heavy nucleus when steady state is reached. Depending on the temperature also a small amount of 15 N can capture a proton and we get the CNO2 cycle instead. Further branching points to get the CNO2 and CNO3 cycle are 17O and 18O. These two cycles are only significant in massive stars. As the CNO cycle is very temperature sensitive, the helium production is concentrated to a very small area in the core. Therefore, we get a steep temperature gradient and energy transport by radiation is impossible. Hence, we have a convective core that mixes material inside the core so rapidly that the core is chemically homogeneous all the time.

11

2.1. STELLAR EVOLUTION 8B

pp1 chain

1H

3He

4He

2H

3H

8B

7Be

8Be

6Li

7Li

1H

pp2 chain

3He

4He

2H

3H

8B

7Be

8Be

6Li

7Li

pp3 chain

1H

3He

4He

2H

3H

7Be

8Be

6Li

7Li

Figure 2.3.: Representation of the three pp chains in the nuclide chart (stable nuclides are shown as shaded squares). CNO1

17F

18F

19F

17O

18O

14O

15O

16O

13N

14N

12C

13C

CNO3

CNO2

17F

18F

19F

17O

18O

14O

15O

16O

15N

13N

14N

15N

14C

12C

13C

14C

17F

18F

19F

17O

18O

14O

15O

16O

13N

14N

12C

13C

CNO4

(p,α)

17F

18F

19F

17O

18O

14O

15O

16O

15N

13N

14N

15N

14C

12C

13C

14C

(α, γ) (p,γ)

(α,p)

(β + ν) (β + νp)

Figure 2.4.: Representation of the four CNO cycles

In Fig. 2.2 the energy production in the pp chains is compared to the energy production in the CNO cycles. At a temperature of about 20 MK the CNO cycles become dominant. Therefore, they are the main process for hydrogen burning in massive stars. The CNO cycles play only a very minor role for the Sun. For both processes, the pp-chains and the CNO cycles, we get an effective reaction of: 4 1H → 4He + 2e+ + 2ν

(2.3)

After the hydrogen fuel in the core is exhausted the nuclear fusion stops. Therefore, the core begins to contracts, as no force counteracts gravity any more. The star evolves off the main sequence. 2.1.4. Evolution after the main sequence The post main-sequence evolution depends on the stellar mass. Figure 2.5 shows the evolution of low-mass and intermediate-mass stars. For a 1 M mass star, the core begins to contract, while a thick hydrogen-burning shell continues to consume available fuel. As the core contracts, its temperature increases. Therefore, the shell-burning produces more energy than the coreburning on the main sequence. This causes the luminosity to increase, the envelope to slightly


12

Figure 2.5.: Schematic diagram of the a 1 M mass (left) and a 5 M mass (right) star in the Hertzsprung-Russell diagram. (Carroll & Ostlie 2007)

expand and the effective temperature to decrease. For a intermediate-mass star the evolution is different. The entire star contracts, which increases the temperature and decreases the radius. Eventually the temperature outside the helium core increases sufficiently to cause a thick shell of hydrogen to burn. This leads to a slight expansion of the envelope and, hence, to a decrease in temperature and luminosity. Afterwards for low- and intermediate mass stars the core is growing, as the shell continues to convert hydrogen to helium. The gravitational energy released causes the envelope of the star to expand and, therefore, the effective temperature decreases. This phase is called the subgiant branch (SGB). With the expansion of the stellar envelope and the decrease in effective temperature a convection zone near the surface develops, which expands deep into the interior of the star. Due to the highly efficient energy transport of convection the star begins to climb the red giant branch (RGB). During the climb on the RGB the convection zone also reaches into regions, which have been chemically altered due to the hydrogen burning. The CNO-cycled material becomes mixed with the pristine material above it. This is called the first dredge-up phase. The abundances on the surface are altered by this phase, which means it can be observed directly in the stellar spectra. Hence, predictions of stellar evolution theory can be tested in this phase. When the conditions in the core are sufficient, the tip on the red giant branch is reached and helium core-burning sets in for stars with masses of more then 0.5 M . This results in an abrupt decrease in luminosity. Helium burning

At this point the evolution of stars < 1.8M differs from the evolution of stars with higher masses. The core of lower-mass stars collapses until it becomes electron-degenerate. The helium-

13


burning sets in almost explosively in the so-called helium flash on the tip of the RGB. A large amount of energy is released in a few seconds, which is absorbed by the overlaying layers, causing some mass loss. Both low-mass and intermediate-mass stars are located on the horizontal branch (HB) during the helium core-burning phase. It is called horizontal branch (HB), as the luminosity of all stars on the HB is very similar. For low-mass stars the observed effective temperature differs, depending on how much envelope is left. Stars that lost much of the envelope on the RGB are found on the blue horizontal branch (BHB) or even on the extreme horizontal branch (EHB), as the burning helium core is closer to the surface. A more detailed discussion of the EHB is given in Chapter 3. Contrary to low-mass stars, which jump to the HB after the helium-flash, intermediate-mass stars evolve in a loop on the HB. Helium-burning takes place via the triple α process: (T1/2 = 6.7 · 10−17 s)

4

He + 4He 8Be

8

4

Be + He →

12

C∗ →

12

12

∗

C

(2.4) (2.5)

C+γ

(2.6)

In the first step of the triple α process an unstable beryllium nucleus (T1/2 = 6.7 · 10−17 s) is produced by the fusion of two α-particles. The nucleus will disintegrate into two helium nuclei, if another α particle is not added immediately. Further α-captures lead to additional reactions during helium burning: 12

C(α, γ) 16O

16

O(α, γ) 20Ne

20

Ne(α, γ) 24Mg

only at high temperatures

Moreover, secondary reactions may occur, which produce free neutrons that play an important role in nucleosynthesis (more details later): 14

N(α, γ) 18F(β + ν) 18O(α, γ) 22Ne

22

Ne(α, n) 25Mg

The ash left behind by helium burning consists mainly of 12C and 16O. Therefore, the stellar core after helium-burning consists mainly of these two nuclides. During their passage along the horizontal branch, many intermediate-mass stars develop instabilities in their outer envelopes leading to long-period pulsations. These stars are called Cepheids. They provide another test of stellar structure theory with the help of asteroseismology, as the pulsations depend sensitively on the internal structure of the star. When the molecular weight of the core has increased to the point that the core contracts again, the most blue-ward point is reached. Shortly afterwards the helium in the core is exhausted and the further evolution is very similar to the evolution after the exhaustion of hydrogen in the core. We get helium and hydrogen shell-burning. This phase is called asymptotic giant branch (AGB). The envelope becomes convective again, resulting in the second dredge-up, which increases the helium and nitrogen content of the envelope. At the upper part of the AGB helium shell-burning begins to turn on and off quasi periodically because the hydrogen-burning shell is dumping ashes onto the helium burning shell. They are called thermal pulses. During this flashes a convective zone is established between the helium-burning shell and the hydrogen-burning shell. For stars with masses > 2M the convection zone reaches deep into the interior of the star resulting in the third dredge-up. For stars with masses smaller than about 8 M on the ZAMS the carbon-oxygen core will never reach a mass and temperature sufficient for further nuclear burning and is, hence, contracting. In the latest stage of evolution on the AGB, a super-wind (maybe due to shell flashes or envelope pulsations) develops with M˙ ∼ 10−4 M yr−1 . This high mass loss makes sure that the stellar core does not experience catastrophic core-collapse. The maximum value of 1.4 M for a completely degenerate core is known as the Chandrasekhar limit. As the cloud (due to


14

the mass loss) around the star expands, it becomes optically thin, exposing the central star. The star is leaving the AGB and its effective temperature increases. The star is called a postAGB star in this phase. A final phase of mass loss is following, in which the envelope is ejected. With only a thin layer of material left, the hydrogen- and helium-burning shells will extinguish. Therefore, no energy production in the star is left, and the luminosity of the star will drop significantly. The hot central object, will cool to become a white dwarf (WD), which is essentially the old red giant’s degenerate core (CO or NeOMg depending on the progenitor mass). Due to the pressure of the degenerate electron-gas the core collapse is stopped and the core is reaching hydrostatic equilibrium. The expanding shell around the white dwarf progenitor is called planetary nebula (PN). The gas is excited or ionized by the ultraviolet light emitted by the hot central star. Typical temperatures of the PN are around 104 K. Only few of the PNs are spherical symmetric. Explanations for the different observed geometries encompass binarity or magnetic fields.

2.1.5. Evolution of massive stars The evolution of more massive stars differs significantly. Figure 2.6 shows the evolutionary tracks for massive stars. For stars with masses larger than 15 M mass loss through stellar winds becomes important throughout the entire life-time. That are rapid mass outflows driven by the strong radiation that erode the outer layers of the star. This changes the evolution significantly. The normal evolution of a not too massive star (M . 15M ) after the main sequence is to become first a red super-giant (RSG, cool, luminous star). Afterwards they become blue super-giants (BSG, hot luminous star) in a blue loop before they explode in a supernova (more details later). More massive stars evolve first to a BSG before they become a RSG. Depending on the mass they explode in a supernova afterwards or become a Wolf-Rayet star before. The most massive stars avoid the RSG stage and evolve into WR stars after a brief BSG phase. Due to the strong winds more massive stars become Wolf-Rayet (WR) stars after the RSG phase. WR stars are hot, very luminous stars with bright emission lines in their spectra. The emission indicates very strong, optically thick stellar winds, with high mass-loss rates. The winds are driven by radiation pressure. Depending on their spectra WR stars are grouped into different classes, which represent an evolutionary sequence of exposure of deeper and deeper layers, as a massive star is peeled off to a larger and larger extent by mass loss: • WNL stars have hydrogen present on their surfaces (with XH < 0.4) and increased He and N abundances, consistent with equilibrium values from the CNO-cycle • WNE stars are similar to WNL stars in terms of their He and N abundances, but they lack hydrogen (XH = 0) • WC stars have no hydrogen, little or no N, and increased He, C and O abundances (consistent with partial He-burning) • WO stars are similar to WC stars with strongly increased O abundances (as expected for nearly complete He burning) Very massive stars become Luminous Blue Variables (LBV). This a very unstable stars with high luminosities showing outbursts accompanied by enormous mass loss. The most famous example in our galaxy is η Carinae. In summary the evolution of massive stars depends very strong on the mass:

15


Figure 2.6.: Evolutionary tracks for non-rotating (dotted lines) and rotating (continuous lines) models for massive stars of different masses (Meynet & Maeder 2003) M . 15M 15M . M . 25M

25M . M . 40M

40M . M . 85M M & 85M

MS(OB) → RSG → (BSG in blue loop? → RSG) → SNII mass loss relatively unimportant . few M during entire evolution MS(O) → BSG → RSG → SNII mass loss is strong during the RSG phase, but not strong enough to remove the whole H-rich envelope MS(O) → BSG→ RSG → WNL → WNE → WC → SN Ib the H-rich envelope is removed during the RSG stage, turning the star into a WR star MS(O) → Of → WNL → WNE → WC → SN Ib/c Of stars are O supergiants with pronounced emission lines MS(O) → Of → LBV → WNL → WNE → WC → SN Ib/c an LBV phase blows off the envelope before the RSG can be reached

After helium-burning, as soon as the conditions in the core are sufficient, massive stars also start further burning-stages, before they explode in a supernova. Carbon burning

Stars with masses larger than 8 M can ignite carbon-burning in their core when Tc > 5 · 108 K and ρc > 3 · 109 kg m−3 . During carbon-burning basically two different reactions take place, both fusing two 12C nuclei: 12

C( 12C, p) 23Na

12

12

20

C( C, α) Ne

[( 12C( 12C, n) 23Mg]

(∼ 50%) (∼ 50%)


16

Moreover, several side reactions exist: 23

Na(p, α) 20Ne,

20

Ne(α, γ) 24Mg,

12

C(p, γ) 13N(β + ν) 13C(α, n) 16O, ...

Carbon burning leaves 16O, 20Ne, 23Na, and 24Mg as ashes behind. Therefore, the result of carbon-burning is in principle an O-Ne-Mg core. The timescale for this phase is in the order of 500 years. Neon burning

As next burning phase, we would expect oxygen-burning via the fusion of two 16O nuclei, as this is the element with the lowest mass in the core. However, before this occurs in stars with masses larger than ∼ 10M that reach temperatures Tc > 109 K, photo-disintegration reactions become important for 20Ne, which are liberating α-particles: 20

Ne(γ, α) 16O

20

Ne(α, γ) 24Mg(α, γ) 28Si

23

Na(α, p) 26Mg(α, n) 29Si

Those α particles can then be captured and produce 24Mg and 28Si. The effective reaction is, therefore, 20Ne + 20Ne → 16O + 24Mg + 4586 keV. Neon-burning leaves mainly 16O, 24Mg, and 28 Si in the core. This phase lasts only for about the order of a year. Oxygen burning

After neon burning terminates, the core of the star consists mainly of oxygen, magnesium and silicon. 16O+ 16O fusion is now the most likely process to occur, as it has the lowest Coulomb barrier (that is the energy barrier due to electrostatic repulsion that two nuclei need to overcome so they get close enough to undergo a nuclear reaction). Stars with masses larger than 10 M reach temperatures higher than 2 · 109 K in the core, sufficient for oxygen burning. 16

O( 16O, p) 31P

16

16

∼ 40%

30

O( O, 2p) Si

16

O( 16O, α) 28Si

16

16

∼ 60%

24

[ O( O, 2α) Mg]

Q M2 ) the mass ratio of both stars. By changing to spherical coordinates (x = r · sin θ cos φ and x2 + y 2 = (1 − cos2 θ)), and moving the origin of the coordinate system to the center of mass of both stars respectively, we can derive for both stars a Roche potential: ! 1 1 2q + 1 + r +q p − λr (1 − ν 2 ) Ω1 = 1 1 2 r1 2 1 − 2λr1 + r1 ! 1 1−q 1 2q + 1 2 Ω2 = +q p − λr + r (1 − ν ) + (6.3) 2 2 r2 2 2 1 − 2λr2 + r22 p with rn = x2n + yn2 + zn2 , λ = sin θ cos φ, and ν = cos θ. To describe the stellar surfaces the equipotential surfaces are used, which consist of the points with the same potential Ω. With decreasing Ω the surface increases until a critical Roche potential Ωcrit is reached that reaches the Lagrange points L1/2/3 . This is called the Roche lobe, which is depending on the mass ratio. Calculation of synthetic lightcurves

For the calculation of the synthetic lightcurves the Wilson-Devinney (WiDe) method is used (Wilson & Devinney 1971). This method uses 12+5n (n is the number of lightcurves at different wavelength bands fitted simultaneously) parameters (see Table 6.1). A lightcurve represents the change of the flux with time or phase. In the WD method the monochromatic flux from both stars together at each phase is summed up. Several physical effects are considered in the calculation of the flux: – Limb darkening (cf. Sect. 5.3) D=

I(0, cos θ) = 1 − x(1 − cos θ) I(0, 1)

(6.4)

63

6.1. ANALYSIS OF (ECLIPSING) BINARIES

Figure 6.2.: Cross-section of some Roche equipotential surfaces at a mass ratio q = 0.17 (Carroll & Ostlie 2007) Table 6.1.: Parameters used for the lightcurve calculation i inclination q mass ratio M2 /M1 with M1 > M2 Ω1 , Ω2 surface potentials T1 , T2 effective temperatures A1 , A2 albedo g1 , g2 gravitational darkening coefficients δ1 , δ2 radiation pressure coefficients L1 (λ), L2 (λ) monochromatic luminosities x1 (λ), x2 (λ) limb darkening coefficients l3 (λ) third light

– Gravity darkening As stars are rotating the effective surface gravity is smaller at the equator than at the poles because of centrifugal forces. This leads to a lower flux. The flux change is given by ( g gl 1.00, for completely radiative envelopes (von Zeipel 1924) Fl = Fp , g= gp ≈ 0.32, for completely convective envelopes (Lucy 1967) (6.5) gl is thereby the local surface gravity and gp the surface gravity at the poles. With the 4 help of the Stephan-Boltzmann law (Fl/p ∼ Tl,p ) and the Planck function, the gravitational darkening factor G can be derived hc

e λTp − 1 Ilocal = hc G= Ipole e λTl − 1

(6.6)

– Reflection effect The reflection effect is a very important effect in close binaries consisting of a hot and a cool

CHAPTER 6. ANALYSIS METHODS

64

star, such as the sdB binaries studied in this thesis. It was already introduced in Sect. 3.3.2. The hot star is illuminating the cool companion resulting in a sinusoidal flux variation, as the visible area of the bright, illuminated side is changing with phase. Physically the illuminated side of the companion is heated up from ∼ 3000 K to temperatures of 10000 to 20000 K depending on the separation and temperature of the hot primary. The flux is, therefore, increasing according to the Stephan-Boltzmann law. In the WD model this effect is considered only in a very simplistic way as a reflection of incoming flux. This is calculated with the help of albedos, which indicate the percentage of flux that is reflected. As we calculate only monochromatic fluxes, it is also not physically inconsistent to get albedos > 0, which results from flux redistributions in the heated hemisphere. We can determine the change in temperature caused by the reflection effect with the help of the Stephan-Boltzmann law and from this the change of flux caused by the reflection effect. hc 1 A2 F1 4 e λT2 − 1 Iref TR = T2 1 + = hc →R= (6.7) F2 Inoref e λTR − 1 – Radiation pressure For hot, luminous stars the radiation pressure on the companion plays an important role. It can even influence the shape of the star. In the most extreme cases, radiation pressure from the companion also affects the shape of the hot primary. More details for the impact of the radiation pressure on the shape of the star can are described in (Haas 1993). In order to calculate the lightcurve the shape of the star is first calculated with the help of the Roche model. This shape is then modified accounting for radiation pressure. Afterwards, each star is divided into small surface elements. For each surface element the flux is calculated including the before mentioned effects. l(Φ) = r2 sin θ∆θ∆Φ

cos γ GDRI cos β

(6.8)

In each phase the flux of the visible surface elements of both stars is summed up, which results in the change of flux with phase. The WiDe method also includes different modes that are suited for different system configurations. In this work we used only WiDe mode 2, which links the luminosity of the companion to its temperature with the help of the Planck function. MORO

There exist several implementations of the WiDe model that allow the calculation of synthetic lightcurves and the fitting of these to observational data. In this work MORO (MOdified ROche program) was used. This program was developed at the Dr. Karl Remeis Observatory. A detailed description of MORO can be found in Drechsel et al. (1995) and Lorenz (1988). In MORO the WiDe method has been modified to account for the effect of radiation pressure on the shape of a star to be able to analyze eclipsing binaries consisting of young, massive stars. The fitting of synthetic lightcurves to the observations is performed with a classical χ2 minimization with the help of the simplex algorithm (Kallrath & Linnell 1987). The simplex algorithm defines a set of m+1 start parameter sets (m the number of parameters), the so-called simplex, around the start parameters that were defined by the user. For each of these parameter sets a synthetic lightcurve is calculated. This synthetic lightcurve is then compared to the observations. From the residuals (dν = lνO − lνC ) the standard deviation σ is calculated. v u n X u n 1 t P σfit (x) = wν dν 2 (x) (6.9) n − m nν−1 wν ν=1

65

6.1. ANALYSIS OF (ECLIPSING) BINARIES

n is the number of points in the lightcurve and wν the weight of each point. The parameter set with the largest standard deviation is discarded and replaced by a new parameter set that is found by fixed operations (reflection, contraction, expansion, shrinkage). This step is repeated until the abort criterion is reached. As always the parameter set with the largest standard deviation is discarded, this algorithm is quite stable and will reach a minimum in any case. This minimum, however, may only be local but not necessarily the global one we look for. Several of the parameters used in the lightcurve analysis are correlated parameters. This can cause severe problems, if too many and inadequate combinations of parameters are adjusted simultaneously. In particular, there is a strong degeneracy with respect to the mass ratio. Besides the orbital inclination, this parameter has the strongest effect on the light curve, and it is highly correlated with the component radii. Therefore, as many parameters as possible have to be fixed at values from theory, or values determined from the spectroscopic analysis. In particular the mass ratio is not adjusted but kept fixed and a possible mass ratio range has to be determined by spectroscopy. For several different mass ratios in the expected range, a number of fits with different start parameters is performed to ensure that the global minimum is found. The solution with the lowest standard deviation is supposed to be the final and best solution. For the error determination the bootstrapping method was used. For this, random data points from the data set are taken and a new fit is performed. This step is repeated about 500 times. The standard deviation of all adjusted parameters in all solutions gives the statistical errors. Orbital period determination

The orbital period is the most fundamental parameter in lightcurve analysis. Additional light variations may arise from pulsations. – FAMIAS1 (Frequency Analysis And Mode Identification For Asteroseismology) For the period determination and correction in continuous lightcurves FAMIAS is an easy to use program. It was developed at the Insituut voor Sterrenkunde, K.U. Leuven by Zima (2008). This program can be used to analyze time-series photometry and spectroscopy. Periodicities are found with the help of a Discrete Fourier transformation. It is also possible to determine the statistical significance of the peaks found in the Fourier periodogram. Moreover, it is possible to pre-whiten the data from periods already determined. This is done by computing a non-linear multi-periodic least-squares fit of a sum of sinusoidals to the data. The fitting formula is X Z+ Ai sin[2π(Fi t + Φi )] (6.10) i

where Z is the zero-point, and Ai , Fi and Φi are amplitude, frequency and phase (in units of 2π) of the i-th frequency respectively. The least-squares fit is carried out with the Levenberg-Marquardt algorithm. The data can then be pre-whitened with the computed fit. – Lomb-Scargle periodogram However, for unevenly sampled or non-continuous lightcurves a Fourier transformation does not work well. For such data, it is preferable to use the Lomb-Scargle method (Press & Rybicki 1989), which estimates a frequency spectrum based on a least squares fit of sinusoid. The periodogram is described by h i2 hP i2  P X(t ) cos ω(t − τ ) X(t ) sin ω(t − τ ) j j j j j j 1  P P + (6.11) Px (ω) =   2 2 2 j cos ω(tj − τ ) j sin ω(tj − τ ) 1

http://www.ster.kuleuven.be/~zima/famias/


66 P

sin 2ωtj

The time-delay τ is defined as tan 2ωτ = P j cos 2ωtj and X(tj ) represent the unevenly j spaced data values. This periodogram can be used to identify the periodicities. 6.1.2. Time dependent spectroscopy From the lightcurve it is only possible to determine relative parameters, as the luminosity ratio, the radii ratio, or the mass ratio. To be able to derive the masses and radii of both components also a spectroscopic analysis is essential. From time-series spectroscopy we can determine in this work only the radial velocity (RV) curve of the primary and the mass function, as all eclipsing binaries under investigation are single-lined. This is due to the huge luminosity difference between both components of the binaries. The semiamplitude of the RV curve K is derived by fitting sine curves to the RV points, which were phased with the period determined from the lightcurve. Due to the short period, a circular orbit is expected, and eccentricity can be neglected. From the semi-amplitude of the RV curve K, together with the period P , the mass ratio q and the inclination i derived by the lightcurve analysis, we can calculate the masses and the separation of the system: P K13 (q + 1)2 2πG (q · sin i)3 M2 = q · M1 r1/2 1 P K1 · + 1 → R1/2 = ·a a= 2π sin i q a M1 =

(6.12) (6.13) (6.14)

This also allows the radii of the stars to be derived, as the lightcurve analysis provides r1/2 /a. 6.1.3. Atmospheric parameters Moreover, the effective temperature, surface gravity, and helium abundance of the primary star can be determined by a quantitative spectral analysis. The helium abundance is determined by modeling the He line profiles. In hot stars the surface gravity can be determined by fitting the wings of the H lines, which are sensitive to the pressure broadening by the Stark effect. The temperature can be derived by the line depth of the hydrogen lines. The maximum depth can be found in A0 stars. For hotter stars the line depth gets shallower, as more and more of the hydrogen is ionized. As Teff and log g both are derived by the hydrogen lines, they are both correlated and cannot be disentangled easily. Therefore, the availability of ionization equilibria is very important, which are only sensitive to the temperature. Unfortunately, in the low-resolution spectra of the sdB binaries we have at our disposal there are no equilibria present. For the spectral analysis we used SPAS (Spectrum Plotting and Analysis Suite), which was developed by Hirsch (2009). This program fits synthetic spectra to the observational data by interpolating in a three-dimensional grid of pre-calculated synthetic spectra. To save computer time, pre-defined wavelength ranges around single lines are fitted. It is possible to fit all lines simultaneously or separately and determine the standard deviation. Moreover, an statistical error determination is possible with the bootstrapping method. SPAS is a re-implementation of FITSB2 by R. Napiwotzki. In contrast to this program SPAS possesses a user-friendly interface and additional functions, like for example it is possible to co-add single spectra, or apply a Doppler shift. A downhill simplex algorithm is employed to find the best possible fit by linear interpolation in the model spectrum grid. It is possible to broaden the model spectra by rotation or macroturbulence. For the determination of the radial velocity a simple combination of Gaussians and Lorentzians are fitted to the spectral lines together with a linear offset.

67

6.2. QUANTITATIVE SPECTRAL ANALYSIS

6.2. Quantitative spectral analysis 6.2.1. Fundamental parameters and abundances The atmospheres of OB stars are characterized by several atmospheric parameters and the elemental abundance. These parameters can be determined by a quantitative spectral analysis. All parameters are determined by fitting the observed spectrum with a grid of synthetic spectra, which was calculated the same way as described in Chap. 8. We used the method introduced by Irrgang et al. (2014) to analyze high-resolution B star spectra in the optical. In contrast to most other methods this method is fitting the complete spectrum at the same time and therefore using all parameter indicators simultaneously. Previously, we used the method described by Nieva & Przybilla (2010) for a quantitative analysis. This method is based on an iterative process to bring all indicators into agreement. Both methods are compatible and rely on the same indicators. However, the previous method is slower, and the new approach allows the analysis of many stars in a short time. In the following the spectral features are briefly discussed, from which the atmospheric parameters are primarily constrained. Effects of parameter variations on strategic spectral lines are also displayed in Fig. 6.3. • Effective temperatures Teff : As already mentioned it is a key parameter for the description of the atmospheric structure. Since the local temperature is crucial for the excitation of the elements, each spectral line is sensitive to the effective temperature. In particular in the UV it can be observed that the number and depth of the spectral lines is changing rapidly with the temperature (see Appendix C). As long as the population of the lower state of a transition is increasing, the line gets strengthened. If most atoms are ionized, the spectral lines are getting shallower. Therefore, the best indicators for Teff are elements showing spectral lines of different ionization stages simultaneously. • Surface gravity log g: The surface gravity determines the pressure and density structure, which implies that in principle all spectral lines are affected. A larger surface gravity also implies a denser plasma, which increases the probability of electron captures by ions and, hence, decreases the degree of the ionization. Therefore, also lines of different ionization stages can be used to constrain log g. In hot stars the surface gravity is primarily determined by fitting the wings of the Balmer lines, which are highly sensitive to log g because they are broadened by the linear Stark effect. However, the strength of the Balmer lines is also very sensitive to the temperature. This means the Balmer lines alone are not sufficient to determine both at the same time, in addition the ionization equilibria have to be used. That is why a method fitting the whole spectrum is very useful to limit the errors. • Microturbulence ξ: As described in Sect. 5.3, the microturbulent velocity is a microscopic parameter, which can affect the strength and shape of all spectral lines. Weak lines have a Gaussian shape. An increasing microturbulent velocity produces a wider shallower Gaussian shape, what does not affect the equivalent width. However, stronger lines get saturated (more details later). This implies that increasing ξ, widens the wavelength range covered by the absorption and reduces the saturation, thus increasing th total absorption. This means that in particular saturated lines are ideal to determine the microturbulence. • Projected rotational velocity v sin(i) and macroturbulence ζ: These macroscopic broadening parameters describe the blurring of spectral lines and can be derived from the shape of spectral lines, preferably from those which are intrinsically sharp, as most metal lines.


68

Figure 6.3.: Effects of changes in effective temperature, surface gravity, microturbulence, and silicon abundance on lines of hydrogen, helium, and silicon. The parameter under consideration is increased in the blue dashed model and decreased in the red dashed-dotted model with respect to the gray solid reference model (Teff = 20 000 K, log(g) = 4.0 dex, ξ = 4 km s−1 , log(n(He)) = −1.15 dex, log(n(Si)) = −4.5 dex) by Teff = ±5000 K (top row), log(g) = ±0.4 dex (second row), ξ = ±4 km s−1 (third row), and log(n(Si)) = ±0.6 dex (bottom row). Adopted from Irrgang (2014).

• Radial velocity vrad : The radial velocity, which is the velocity of the star in the line-ofsight, leads to a shift of the spectrum due to the Doppler effect. The amount of the shift can directly be translated in a Doppler velocity (λ0 = λ0 (1 − vc )).

69

6.2. QUANTITATIVE SPECTRAL ANALYSIS

2.5

log g

3

3.5

4

4.5

15 12 4.5

9

7

4.4

5 4.3

4 4.2

4.1

4

log Teff

Figure 6.4.: Evolutionary tracks by Georgy et al. (2013) in the Teff − log g diagram for different initial masses (M ) together with the position of HD 271791

• Elemental abundances: The abundances of all elements besides H and He are small. The metals, therefore have little impact on the continuum in hot stars. However, the number of metal absorbers has a strong effect on the strength of lines, which are therefore good indicator for elemental abundances. The relation between the strength of spectral and elemental abundances is, however, not linear. It can be described by a curve of growth, which shows three domains of behavior. For weak lines the growth is linear, which are therefore ideal to determine abundances. For stronger lines saturation is observed, which means the lines become more insensitive to abundance changes. Even stronger lines begin to develop damping wings as seen, e.g. in the Balmer lines, which lead again to an increase of the equivalent width. For a detailed discussion see Gray (2005) pp.326-335.

6.2.2. Mass, age and radius of the star The atmospheric parameters (Teff and log g) can also be used for the determination of the mass, age and radius of the star with the help of stellar evolution models. The evolution of a star in the the Teff -log g diagram (see Fig. 2.6) mostly depends on the initial mass. As can be seen in Fig. 6.4 the tracks run parallel depending on the initial mass of the star crossing the Teff -log gdiagram as they evolve. Therefore, the position in the Teff − log g-diagram can be used to derive the fundamental stellar parameter mass Minitial , M and age τ . The luminosity L can be derived T 4 /T 4 from L/L = M/M effg/g eff . In the last years it became clear that the rotation of a star is an important parameter for the evolution of a star, which has, hence, to be considered, too. As the inclination of the system is typically unknown, we can only use a statistical approach and use the spherically averaged value π/4 for the inclination when matching v sin(i) to the equatorial velocity vrot predicted by the evolutionary tracks. In this work we determined the parameters (M , age, L) from fitting single-star evolutionary tracks that account for stellar rotation by Georgy et al. (2013) to the Teff and log g determined by the spectral analysis. The radius can be calculated by the from the surface gravity and the determined stellar mass R = g/GM . The errors in the parameters have been determined from the error in Teff and log g.


70

6.2.3. Distances It is possible to derive the distance to the star, with the help of a synthetic spectrum F (λ), which represents the flux coming from the surface of the star. This flux is distributed uniformly in a sphere with the radius equals the distance d. Applying flux conservation we can determine the angular diameter by using the measured flux f (λ): 4πθ2 f (λ) = 4πR2 F (λ)

(6.15)

If the stellar radius R is known, this can be used to derive the distance d = 2R/θ, assuming small angles. Instead of using monochromatic fluxes, it is more convenient to use photometric measurements in a suitable filter: The corresponding magnitude magx to an arbitrary photometric passband can be derived by   R∞ rx (λ)f (λ)λdλ   0  + magref (6.16) magx = −2.5 log  x ∞  R rx (λ)f ref (λ)λdλ 0

using, a suitable reference star, e.g. Vega. Thereby is rx (λ) the system response function. More details about the distance determination together with an example can be found in Nieva & Przybilla (2014). However, the existence of interstellar dust and gas leads to an absorption of photons along the line of sight, which is called interstellar extinction. This causes also a reddening and therefore a change in the slope of the spectral energy distribution (SED). This effect has to be accounted for with the help of a reddening factor 10−0.4A(λ) , with A(λ) the extinction in magnitude at wavelength λ. Fitzpatrick (1999) gives a relation for A(λ) as a function of the color excess E(B−V ) and the extinction parameter RV = A(V )/E(B−V )) = (3.1 for the diffuse interstellar medium, often used for Galactic interstellar extinction), which can be used to account for the extinction Mcorr (X) = M (X) + A(X)E(B − V ). Therefore, we determine E(B-V) as well as the distance by fitting the measured photometry in several passbands.

6.3. Stellar kinematics The spectroscopic analysis facilitates the distance d to the star and its radial velocity vrad to be derived. The Hipparcos satellite launched in 1989 and operated until 1993, measured the positions and proper motions in right ascension (µα cos(δ)) and declination (µδ ) of more than 180000 bright stars with a precision of about 1 mas (milli arc second). For bright stars also less accurate proper motion measurements are available covering typically much larger time spans. The Gaia spacecraft launched in December 2013, however, is measuring the parallax and proper motion of about 1 billion stars brighter than 20th magnitude at the moment with an accuracy < 20µas. This may revolutionize the stellar astrophysics, as for all brighter stars distances and proper motions will be available. With the help of the proper motions and the radial velocity vrad the full six-dimensional kinematics of the object at present time can be derived. The Galactic rest-frame velocity can then √ be determined by the three-dimensional velocities v = (vx , vy .vz ) → vGrf = v · v. By using a model p for the gravitational potential of the Galaxy Φ(x) the star’s local escape velocity vesc (x) = −2Φ(x), from which we can conclude whether the star is still bound to the Galaxy by comparing the escape velocity to the rest-frame velocity. In this work we used the three different models that were described by Irrgang et al. (2013):

71

6.3. STELLAR KINEMATICS

• a revised Galactic gravitational potential by Allen & Santillan, Model I in Irrgang et al. (2013) • potential with a Miyamoto & Nagai bulge and disk component and a Navarro, Frenk, & White dark matter halo, Model III in Irrgang et al. (2013) • potential with a Miyamoto & Nagai bulge and disk component and a truncated, flat rotation curve halo model They were determined by fitting different models with certain parameters to the rotation curve of the Milky Way and other constraints. With the help of the potential it is also possible to trace the orbit of the star back in time. The intersection of the star’s orbit with the Galactic disk is possibly p the birthplace of the star, which can be characterized by the Galactocentric radius rd = x2 + y2 . Moreover, the flight time τ and the ejection velocity vej defined as the velocity at disk intersection relative to the rotating Galactic disk can be determined with this method. These parameters can be used to check how realistic the runaway ejection models in this case are and if the evolutionary age of the runaway star enables an ejection scenario at all. Uncertainties in the input parameters are obtained from 100000 Monte Carlo runs for different Milky Way mass models using different initial values for the parameters within the errors for them.

7. Analysis of hot subdwarfs with cool companions After the introduction into the basic principles and the analysis methods, I will now come to the actual analysis done in my thesis. I worked with two very different groups of post-common envelope systems: low-mass and high-mass systems. In this chapter I will describe the analyses of a special group of low-mass post common-envelope systems, sdB+dM binaries. They were introduced in Chapter 3. I will first discuss the MUCHFUSS project, which amongst other things aims at discovering such systems. Afterwards I present the analysis of some individual sdB+dM binaries. I conclude with a comparison of the known reflection effect binaries with the known eclipsing WD+dM systems.

7.1. The MUCHFUSS project The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims to find hot subdwarf stars with massive compact companions like massive white dwarfs (> 1.0M ), neutron stars or stellar mass black holes (see Geier et al. 2011a, 2015). Hot subdwarf stars were selected from the Sloan Digital Sky Survey (SDSS) by colour and visual inspection of the spectra. Hot subdwarf stars with high radial velocity variations were selected as candidates for follow-up spectroscopy to derive the radial velocity curves and the binary mass functions of the systems. The selection criteria turned out to be not only suitable to find massive, compact companions but also binaries with low-mass companions with short periods were discovered. With the help of a photometric follow-up, it is possible to distinguish between low-mass, white dwarf or main-sequence companions. 7.1.1. Target selection The target selection of the MUCHFUSS project was discussed by Geier et al. (2011a). The selection criteria were applied to the SDSS Data Releases 6 and 7 (Adelman-McCarthy et al. 2008; Abazajian et al. 2009). Hot subdwarf candidates were selected by applying a color cut to SDSS photometry. All point source spectra within the colours u − g < 0.4 and g − r < 0.1 were selected and downloaded from the SDSS Data Archive Server1 . Objects fainter than g = 18.5 mag have been excluded because of insufficient quality. The SDSS spectra are coadded from at least three individual integrations with typical exposure times of 15 min taken consecutively. We have obtained those individual spectra for all selected stars. Moreover, second epoch medium resolution spectroscopy (R = 1800 − 4000) was obtained from SDSS as well as our own observations, using ESO-VLT/FORS1, WHT/ISIS, CAHA-3.5m/TWIN and ESONTT/EFOSC2 (see Geier et al. 2011a). The RVs have been measured as described by Geier et al. (2011b). Each single fit has been inspected visually and outliers caused by cosmic rays and other artefacts have been excluded. We selected all objects with RVs discrepant at the formal 1σ-level and found 81 candidates for RV variability in SDSS DR 6 (Geier et al. 2011a) and 196 candidates in SDSS DR 7 (Geier et al. 2015). The highest RV shift over the corresponding 1

http://das.sdss.org

73

CHAPTER 7. ANALYSIS OF HOT SUBDWARFS WITH COOL COMPANIONS

74

Figure 7.1.: Highest radial velocity shift between individual spectra plotted against time difference between the corresponding observing epochs. The filled red diamonds mark sdO/B binaries with known orbital parameters (Kupfer et al. 2015), while the filled black circles mark the rest of the hydrogen-rich sdB, sdOB and sdO sample of RV variable stars (Geier et al. 2015).

time difference is shown in Fig. 7.1. To determine the true nature of the unseen companion, the period and the RV semi-amplitude has to be measured. Even so the inclination is still undetermined. This means the mass of the companion is not constrained very well. Often it is not possible to distinguish between a low-mass stellar or a white dwarf companion. Only if the minimum mass is more than 0.45 M , we can exclude a stellar companion, as it should be visible in the spectrum (Lisker et al. 2005). With the help of a photometric follow-up, we can determine the nature of the companion and the period of the system, if light variations are visible. Even without variations, it can help to select interesting targets. Moreover, we can derive the fraction of reflection effect binaries and close substellar companions around hot subdwarf stars, as the targets are RV selected. 7.1.2. Light variations and their observations with BUSCA Observations with BUSCA

Based on the target selection of the MUCHFUSS project (Geier et al. 2011a) we selected targets with radial velocity variations on very short time scales (smaller than 0.1 d) for a photometric follow-up. The MUCHFUSS photometric follow-up (more details on the analysis in Sect. 7.8) was done with BUSCA (Bonn University Simultaneous CAmera; see Reif et al. 1999) on the 2.2m-telescope located at the Calar Alto Observatory in Spain. This instrument turned out to be perfect for our purposes, as it is possible to observe in four bands simultaneously.

75

7.1. THE MUCHFUSS PROJECT

Figure 7.2.: Light path in the BUSCA instrument and transmission curve of the four different channels (UB , BB , RB , IB ). Table 7.1.: Log of observations with BUSCA Year/Month/Date 2010/06/11 2010/09/29-2010/10/03 2011/02/25-2010/03/01 2011/05/30,31;2011/06/03 2011/09/28-2011/10/02 2011/10/17-21 2012/01/13,14 2012/10/10-14

P.I. SG SG SG OC SG OC SG SG

Observer VS VS & EZ VS VS RG VS EZ VS

The observers and P.I.s of the observation are: OC (Oliver Cordes), SG (Stephan Geier), RG (Raoul Gerber), VS (Veronika Schaffenroth), EZ (Eva Ziegerer)

The light is splitted by a beam splitter into four different arms, which can be directly used without a filter (UB , BB , RB , IB ). The transmission curve of the four channels is displayed in Fig. 7.2. To distinguish between different effects causing light variations, lightcurves in several wavelength bands are highly important. We did not use any filters but used the intrinsic transmission curve given by the beam splitters, as that way all visible light is used and no light is wasted. The data was taken in several runs listed in Table 7.1. For each star a lightcurve between 1.5 and 2.5 h with exposure times from 30 to 180 seconds was taken to check for any light variations. BUSCA allows to observe in windows to decrease the read-out time to about 15-20 seconds compared to a full-frame read-out time of about two minutes. Therefore, we observed our target and four comparison stars in 60 x 60 pixel windows to perform relative photometry to correct for the changing airmass, changing conditions, and clouds. The reduction was done using the aperture photometry package provided by IRAF. In total we found 6 stars showing light variations out of 59 checked systems (more details in Sect. 7.8.2). This variations are shown in Fig. 7.35. Lightcurve variations or not?

There are several effects that lead to light variations of hot subdwarf binaries, and if the lightcurve shows periodic variation we can restrict the nature of the companion. One of the possible effects is the so-called reflection effect. It results from a huge temperature difference of both components and rather similar radii and is for this reason visible, if the companion is a low mass main-sequence star or even a brown dwarf. The companion is heated


1.06

i=70 i=50 i=30 i=10 WD:90 WD:70

1.04 1.02 1 normalised flux

76

0.98 0.96 0.94 0.92 0.9 0.88 0.86 0

0.2

0.4

0.6

0.8

1

phase

Figure 7.3.: Lightcurve models in RB of a typical HW Virginis system at different inclinations and of an sdB binary system with a low mass WD with the same period and RV semi-amplitude at 90◦ and 70 ◦ together with a typical non-detection lightcurve.

up on one side due to the immense radiation of the sdB. Therefore, the contribution of the companion to the total flux of the system is changing with the phase and is apparent as a sinusoidal variation with a period equal to the orbital period. Due to the short periods found for these systems, which result from the formation by a common envelope, and the similarity of the radii, sdB+dM systems have a high probability to be eclipsing. Such systems are of high value because they allow to determine the masses and radii of both components by a combined photometric and spectroscopic analysis. Moreover, the separation of the system can be measured. Eclipsing binaries with low-mass stellar companions or substellar companions are called HW Virginis systems after their prototype. The reflection effect is also visible at rather small inclinations, if the period is small. In Fig. 7.3 one can see how the amplitude of the reflection effect changes with the inclination for the parameters of a typical HW Vir system compared to a typical non-detection lightcurve. Even for an already very unlikely inclination of 10◦ , we would expect variations of almost 2%, which would be possible to be seen in the lightcurve. The reflection effect is easily recognizable, if a lightcurve in several bands is available, as this effect depends on the wavelength and is usually getting bigger in the redder bands, because the temperature of the heated side is not as hot as the sdB and, hence, the hot side of the companion is brighter in the redder bands. Due to the smaller radius the reflection effect is not visible in sdB+WD systems, as can be seen in Fig. 7.3 for the example of a low-mass WD, which has, therefore, a rather large radius compared to more massive ones. A different lightcurve variation occurs in short period sdB binary systems with white dwarf companions. The close companion distorts the subdwarf, which is, hence, not spherical any more, but has an ellipsoidal shape. This effect is, therefore, called ellipsoidal deformation and manifests itself in a sinusoidal variation with half the orbital period. The variation gets larger with shorter period of the system and a more massive white dwarf companion. It is easily distinguishable from the reflection effect, even if the period is not known, as the amplitude of the ellipsoidal deformation is wavelength independent.

7.2. ECLIPSE TIME VARIATIONS IN J0820

0.07

80

0.06

70 60

0.05

50 0.04

K [km/s]

relative semi-amplitude A

77

0.03

40 30

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20

0.01

10

0

0 0

10

20

30 40 inclination

50

60

70

0

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20

30 40 inclination

50

60

70

Figure 7.4.: Expected relative semi-amplitude of the reflection effect in RB and expected semiamplitude of the radial velocity of the hot subdwarf for different inclinations for the RB band for the parameters of a typical HW Virginis system like the prototype HW Vir (+) and for an sdB+BD system like J1622 (x) with the functions given by Eq. (7.5) and (7.6).

Moreover, recently unperiodical light variations in He-sdO stars were found (Green et al. 2014b). It is not yet clear were this strange variations come from but they are similar to variations found in cataclysmic variables. Moreover, the reason for the observed radial velocity variations in HesdOs is not understood, as no periodicities can be found. We found also one He-sdO showing such strange light variations (see Fig. 7.35f). In the following we show at first the analysis of several newly discovered eclipsing sdB PCEB systems with substellar companions, substellar companion candidates or low-mass main sequence companions. Afterwards we summarize the analysis of the photometric follow-up of the MUCHFUSS project. The last section gives some statistics of the period and mass distribution of the hot subdwarfs of spectral type B with cool,low-mass companions and a comparison with systems consisting of white dwarfs and low-mass companions, which are the successors of sdB with low-mass companions.

7.2. Eclipse time variations in J0820 The fist HW Virginis system found in the course of the MUCHFUSS project was J08205+0008 (hereforth abbreviated J0820, Geier et al. 2011c; Schaffenroth 2010). As the spectroscopic follow-up suggested a short period of this system of 0.096 d and a very low minimum mass for the companion, this system was prioritized for a photometric follow-up. The observations with the Flemish 1.2 m Mercator Telescope on La Palma, Canary Islands, showed a deep primary and shallow secondary eclipses superimposed on a strong reflection effect in the lightcurves. The spectroscopic and photometric analysis confirmed the first unambiguously detected substellar object (Mcomp = 0.045 − 0.068M ) around an sdB star. Eclipsing binaries are with such short periods ideal for eclipse timing. This facilitates small third bodies, like for example planets, in the system to be detected. Therefore, we obtained more photometric data with BUSCA and with the 1m-telescope located at the South African Astronomical Observatory using the SAAO STE3 CCD, a 512x512 detector, which has a read out time of only about 5 s in the 2x2 prebinned mode. The eclipse times of the observations with the SAAO STE3 CCD were measured by the bisected chords method – essentially measuring the mid-points of a number of chords joining eclipse ingress and egress curves and running parallel to the time axis in a magnitude/time plot. These


78

Figure 7.5.: Different cases in an O-C diagram. See text for further explanations (Lutz 2011).

mid-points always lie very close to a line perpendicular to the time axis, indicating eclipse symmetry, and such a fit has been demanded in every case. Further details about the reduction and analysis methods are discussed in (Kilkenny 2011). For BUSCA the eclipse minima were determined with another method. One observation of an eclipse was extracted and shifted to zero. Afterwards, this reference eclipse was moved across the complete lightcurve in given time steps and the χ2 in each time step was measured. The respective χ2 minimum, which corresponds to the eclipse minimum, is then measured by fitting a Gaussian to the χ2 distribution. In order to compare the eclipse times from different instruments and observation runs the times are converted from UTC to BJD (Eastman et al. 2010, http://astroutils.astronomy.ohio-state.edu/time/utc2bjd.html). Table 7.2 summarizes the measured eclipse times together with the cycle numbers. In order to determine these numbers the period was measured with the help of a Lomb-Scargle periodogram (see Sect. 6.1.1). The eclipse with cycle number 0 was taken as reference point. Therefore, we get an improved ephemeris: BJD = 2455942.46813(5) + 0.096240737(2) · E

(7.1)

Starting from there the cycle number is calculated as E = can be derived:

T0 −T . P

O-C = (T − (T0 + EP ) = T − T0 − EP

From this also an O-C diagram (7.2)

1

2 3

1 MP G 3 PP sin i sin(2πE/PP + Φ) = ∆t0 + ∆P0 E + P0 P˙ E 2 + 2 1 2 · 2 c (MsdB + Mcomp + MP ) 3 4 3 π 3 There are several effects, which can lead to variations in the O-C diagram (see Fig. 7.5). An error in the zero point T0 will lead to an offset. Any inaccuracies in the period can immediately be detect in the O-C diagram, if a linear slope is visible. The correction to the period can then be calculated by the slope of the straight line. Moreover, changes of the period can be detected, if a parabola is visible in the O-C diagram, An downward open parabola implies a period decrease. Another possible effect is an orbital motion caused by third body in the system. This will cause a sinusoidal change in the O-C diagram.

79

7.2. ECLIPSE TIME VARIATIONS IN J0820

10

5

O-C [s]

0

-5

-10

-15

-20 -800 -600 -400 -200

0

200

400

600

800

1000 1200

BJD - 2455942

Figure 7.6.: O-C curve of J0820

i=90oo i=50o i=10

140 120

MP

100 80 60 40 20 0 0

500

1000 1500 2000 period [d]

2500

3000

Figure 7.7.: Detection limit of the timing method for different inclinations assuming an 10 s error in our measurements and a time-base of 1610 d.

The amplitude of this sine curve can be calculated from the mass function and depends of the masses of the third body MP , the masses of both components of the binary MsdB , Mcomp , the period of the third body PP , and inclination i, and the speed of light c. The O-C curve of the sdB+BD system J0820 is given in Fig. 7.6. The baseline of the O-C diagram is 5.3 yr. The period was already adjusted so that no slope is visible, which constrains the period to about 40 µs. No variation in the O-C diagram is recognisable. This means we cannot detect an period


80

Table 7.2.: Eclipse minima of J0820, the positive numbers were observed with the SAAO STE3 CCD, the negative observation numbers with BUSCA cycle number E 0000 0001 3108 4032 4042 4093 4094 4466 4497 4902 4964 7751 7761 7792 8030 8061 8632 8653 -8071 -8040 -7606 -7605 -7604 -3367 -3326

T [BJD] 2455942.46813 2455942.56448 2456241.58437 2456330.51090 2456331.47326 2456336.38149 2456336.47781 2456372.27931 2456375.26275 2456414.24030 2456420.20731 2456688.43014 2456689.39253 2456692.37602 2456715.28130 2456718.26478 2456773.21823 2456775.23928 2455165.70928 2455168.69268 2455210.46121 2455210.55741 2455210.65364 2455618.42562 2455622.37155

error 0.00005 0.00001 0.00002 0.00003 0.00002 0.00003 0.00004 0.00001 0.00008 0.00005 0.00004 0.00002 0.00005 0.00002 0.00005 0.0001 0.00005 0.00003 0.00005 0.00005 0.00005 0.0005 0.0005 0.00005 0.00005

change or third body in the system yet. We have an error of about 10 s in the system, from which we can give an upper limit for a third body in the system depending on the period and inclination (see Fig. 7.7).

7.3. J1920 – A new typical HW Virginis system In the course of the photometric follow-up we discovered a new HW Virginis system J192059+372220 (J1920). The lightcurve is shown in Fig. 7.35c. It shows a prominent reflection effect and grazing eclipses. We also started a spectroscopic follow-up and got 39 medium resolution (R ∼ 4000) spectra with the TWIN spectrograph on the 3.5m-telescope at Calar Alto and 11 spectra from the ISIS spectrograph at the William Herschel Telescope at the Roque de los Muchachos Observatory on La Palma with the same resolution. Those spectra were used to determine the radial velocity curve. The RV was measured using SPAS (Hirsch 2009) by fitting Gaussians and Lorentzians to the Balmer and helium lines. Due to the short period a circular orbit was assumed and, therefore, a sine function was fitted to the measured RVs to determine the semi-amplitude K = 59.8 ± 2.5 km s−1 and the systemic velocity γ = 16.7 ± 2.0 km s−1 and the period P = 0.168876 d. The results are summarized in Table 7.3. The spectra were, moreover, used to determine the atmospheric parameters by fitting synthetic spectra, which were calculated using LTE model atmospheres with solar metallicity and metal line blanketing (Heber et al. 2000), to the Balmer and helium lines.

81

7.3. J1920 – A NEW TYPICAL HW VIRGINIS SYSTEM

100

radial velocity in km s-1

80 60 40 20 0 -20 -40 -60

residuals

40 20 0 -20 -40 0

0.25

0.5 orbital phase

0.75

1

Figure 7.8.: Radial velocity curve of J1920 with the best sine fit. The residuals are shown in the lower panel.

Table 7.3.: Results and parameter of J1920 coord. g’ K γ P a Teff log g log y i MsdB Mcomp

ep=2000 [mag] [km s−1 ] [km s−1 ] [d] [R ] [K] [cgs] [◦ ] [M ] [M ]

19 20 59 +37 22 20 15.58 59.8 ± 2.5 16.8 ± 2.0 0.168876 ± 0.00035 1.078 ± 0.0449 27500 ± 1000 5.4 ± 0.1 -2.5 ± 0.25 67 0.47 0.116 ± 0.007

Each spectrum was fitted separately. In other HW Vir systems an apparent change of the atmospheric parameters with the phase was found (Schaffenroth et al. 2013) due to contaminating light from the heated hemisphere of the companion. As the S/N is high enough, we do not see this effect and we, therefore, averaged all single values. The results can be found in Table 7.3. The parameters are with an effective temperature of Teff = 27500 ± 1000 K and a surface gravity of log g = 5.4 ± 0.1 typical for an sdB lying on the extreme horizontal branch. Unfortunately, we do not have enough photometric data to measure the period from the lightcurve. Also the S/N of our data is not high enough for a proper lightcurve analysis. A


82

preliminary analysis using MORO (MOdified ROche program, see Drechsel et al. 1995), however, showed that the inclination must be about 67◦ . With the help of this information, we are able to calculate the separation of the system and the mass of the companion, assuming a canonical mass of 0.47 M for the sdB, from the mass function. Accordingly, the companion has a mass of 0.116 M and is, therefore, a late M dwarf, like the companions of all but two of known HW Vir systems.

7.4. J1622 – A subdwarf B star with brown dwarf companion2 Here, we report on the discovery of the second short period eclipsing hot subdwarf binary with a substellar companion found in the course of the MUCHFUSS project. As mentioned above this object was found in the photometric follow-up. As the RV curve suggested a short period of only 1.65 h, this was our primary target. In this section, we describe the spectroscopic and photometric observations in Sect. 7.4.1 and their analysis in Sect. 7.4.2 (spectroscopy) and 7.4.4 (photometry). Evidence for the brown dwarf nature of the companion is given in Sect. 7.4.4 and the lack of synchronization of the sdB star is discussed in Sect. 7.4.5. Finally, we conclude and present suggestions on how to improve the mass determination. 7.4.1. Observations Spectroscopy

The SDSS spectra of SDSS J162256.66+473051.1 (J1622 for short, also known as PG1621+476, g’=15.96 mag) showed a radial velocity shift of 100 km s−1 within 1.45 h. Therefore, the star was selected as a high priority target for follow-up. The eighteen spectra were taken with the ISIS instrument at the William Herschel Telescope on La Palma, from 24 to 27 August 2009 at medium resolution (R∼4000). Additional 64 spectra with the same resolution were obtained with the TWIN spectrograph at the 3.5 m telescope at the Calar Alto Observatory, Spain, from 25 to 28 May 2012. Moreover, ten higher resolution spectra (R∼8000) were observed with ESI at the Keck Telescope, Hawaii, on 13 July 2013. The TWIN and ISIS data were reduced with the MIDAS package distributed by the European Southern Observatory (ESO). The ESI data was reduced with the pipeline Makee3 . Photometry

When the RV-curve from the ISIS spectra showed a short period of only 0.069 d, a photometric follow-up was started. The object J1622 was observed with the Bonn University Simultaneous Camera (BUSCA) at the 2.2 m telescope at the Calar Alto Observatory. The instrument BUSCA (Reif et al. 1999) can observe in four bands simultaneously. We did not use any filters but we used instead the intrinsic transmission curve given by the beam splitters, which divides the visible light into four bands UB , BB , RB , and IB (implying no light loss). Four sets of lightcurves, each covering one orbit of J1622, were obtained on 12 June 2010, 29 September 2010, 28 February 2011, and 1 June 2011. They were reduced by using the aperture photometry package of IRAF. As the comparison stars have different spectral types, we observed a long-term trend in the lightcurve with changing air mass due to the different wavelength dependency of atmospheric extinction, which cannot be corrected. 2 3

This chapter is based on Schaffenroth et al. (2014c) http://www.astro.caltech.edu/~tb/ipac_staff/tab/makee/

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7.4. J1622 – A SUBDWARF B STAR WITH BROWN DWARF COMPANION

1

normalized light

normalized light

1

0.9

0.8 0.04 residuals

residuals

0.8 0.04

0.9

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0.6

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1 1.2 orbital phase

1.4

1.6

0.4

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0.8

1 1.2 orbital phase

1.4

1.6

Figure 7.9.: Phased BUSCA lightcurve in BB and RB of J1622. The solid line demonstrates the best-fit model. In the bottom panel, the residuals can be seen.

7.4.2. Spectroscopic analysis Radial velocity curve

The radial velocities were measured by fitting a combination of Gaussians, Lorentzians, and polynomials to the Balmer and helium lines of all spectra, which are given in Table 7.6. Since the phase-shift between primary and secondary eclipses in the phased lightcurve (see Fig. 7.9) is exactly 0.5, we know that the orbit of J1622 is circular. Therefore, sine curves were fitted to the RV data points in fine steps over a range of test periods. For each period, the χ2 of the best-fit sine curve was determined (see Geier et al. 2011b). All three datasets were fit together. The orbit is well covered. Figure 7.10 shows the phased RV curve with the fit of the best solution. It gives a semi-amplitude of K = 47.2 ± 2.0 km s−1 , a system velocity of γ = −54.7 ± 1.5 km s−1 , and a period of 0.0696859 ± 0.00003 d. The period is consistent with the period from the photometry (see Sect. 7.4.3) and is the second shortest ever measured for an sdB binary. Atmospheric parameters

The atmospheric parameters were determined by fitting synthetic spectra, which were calculated using LTE model atmospheres with solar metallicity and metal line blanketing (Heber et al. 2000), to the Balmer and helium lines using SPAS (Hirsch 2009). of the HW Vir stars and similar non-eclipsing systems, it was found that the atmospheric parameters seemed to vary with the phase (e.g. Schaffenroth et al. 2013), as the contribution of the companion to the spectrum varies with the phase. Therefore, all spectra were fitted separately. Figure 7.11 shows the effective temperature and the surface gravity determined from the TWIN spectra plotted against orbital phase. No change with the orbital phase can be seen. Therefore, we co-added all 64 TWIN spectra and derived the atmospheric parameters (Teff = 29000 ± 600 K, log g = 5.65 ± 0.06, log y = −1.87 ± 0.05). In Fig. 7.12 the best fit to the Balmer and helium lines of the co-added spectrum is shown. In Fig. 7.13, the position of J1622 in the Teff − log g diagram is compared to those of the known HW Vir systems and other sdB binaries. It is worthwhile to note that all of the HW Vir systems, but two, which have evolved off the EHB, have very similar atmospheric parameters.


84

40 20 radial velocity in km s-1

0 -20 -40 -60 -80 -100 -120 -140

residuals

40 20 0 -20 -40 0

0.25

0.5 orbital phase

0.75

1

Figure 7.10.: Radial velocity plotted against orbital phase of J1622. The radial velocity was determined from the SDSS, ISIS, TWIN, and ESI spectra. All spectra were fitted together. The stars mark the SDSS spectra, the dots the TWIN spectra, the filled squares the ISIS spectra, and the open squares the ESI spectra. The errors are formal 1-σ uncertainties. The lower panel shows the residuals.

Those systems cluster in a distinct region of the Teff − log g diagram. Unlike the HW Vir stars, other sdB binaries are distributed more or less uniformly across the extreme horizontal branch (see Fig. 7.13). In this respect, J1622 turns out to be a typical HW Vir system. Due to their higher resolution, the ESI spectra are suitable to measure the rotational broadening of spectral lines of the sdB. We co-added all 10 spectra and determined the projected rotational velocity of the sdB primary by adding a rotational profile to the fit of the Balmer and helium lines. The other atmospheric parameters were kept fixed to the values determined from the TWIN spectra. The best fit for vrot sin i = 71 ± 7 km s−1 is displayed in Fig. 7.14. Surprisingly, the projected rotational velocity is only about two thirds of the one expected for tidally locked rotation of the hot subdwarf primary. This issue is further discussed in Sect. 7.4.5. 7.4.3. Photometric analysis The BUSCA lightcurves clearly show a strong reflection effect and grazing eclipses, as can be seen in Fig. 7.9. Unfortunately, the signal-to-noise of the UB and IB lightcurves is insufficient, so that only the BB and RB lightcurves were used for the analysis. The ephemeris was determined from the BUSCA lightcurves by fitting parabolas to the cores of the primary eclipses. The period was derived with the help of the Lomb-Scargle Algorithm (Press & Rybicki 1989). The ephemeris of the primary minimum is given by HJD = 2455359.58306(2) + 0.0697885(53) · E

85


32000

6.1 6

31000 5.9 5.8 log g

Teff in K

30000

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phase

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1

phase

Figure 7.11.: Effective temperature and surface gravity plotted over the phase of J1622. Teff and log g were determined from the TWIN spectra. The errors are statistical 1-σ errors. The lines represent the parameters from the co-added spectrum with the errors.

(thereby E is the eclipse number, see Drechsel et al. 2001). The phased lightcurves are shown in Fig. 7.9 . The lightcurve analysis was performed by using MORO (MOdified ROche Program, see Drechsel et al. 1995), which calculates synthetic lightcurves, which were fitted to the observation. This lightcurve solution code is based on the Wilson-Devinney approach (Wilson & Devinney 1971) but uses a modified Roche model that considers the radiative pressure of hot binaries. More details of the analysis method are described by (Schaffenroth et al. 2013) and Chapter 6. The main problem of the lightcurve analysis is the large number of parameters. To calculate the synthetic lightcurves, 12+5n (n is the number of lightcurves) parameters that are not independent are used. Therefore, strong degeneracies exist, in particular in the mass ratio, which is strongly correlated with the other parameters. The mass ratio is, therefore, fixed, and solutions for different mass ratios are calculated. To resolve this degeneracy, it is, moreover, important to constrain as many parameters as possible from the spectroscopic analysis or theory. From the spectroscopic analysis, we derived the effective temperature and the surface gravity of the sdB primary. Due to the early spectral type of the primary star, the gravity darkening exponent can be fixed at g1 = 1, as expected for radiative outer envelopes (von Zeipel 1924). For the cool convective companion, g2 was set to 0.32 (Lucy 1967). The linear limb darkening coefficients were extrapolated from the table of Claret & Bloemen (2011). To determine the quality of the lightcurve fit, the sum of the deviations from each point to the synthetic curve is calculated, and the solution with the smallest sum is supposed to be the best solution. The difference between the solutions for the different mass ratios is unfortunately small, as expected. Therefore, we cannot determine a unique solution from the lightcurve analysis alone and adopted the solution closest to the canonical mass for the sdB star. The corresponding results of the lightcurve analysis are given in Table 7.4 with errors determined by the bootstrapping method. The lightcurves in the BB and RB band are displayed in Fig. 7.9 with the best-fit models for these parameters. The apparent asymmetries of the observed lightcurve can not be modelled, but we are not sure if this effect is real or is due to uncorrected long-term trends in the photometry (see Sect. 7.4.1). The parameters of the system resulting from the adopted solution with the mass function are summarised in Table 7.5. The uncertainties result from error propagation of the errors of K, P , and i.


He I 4922 He I 4472 He I 4026

86

Hβ Hγ Hδ Hε H8 H9 H 10 H 11

−40

−30

−20

−10

0 ∆λ[Å]

10

20

30

40

Figure 7.12.: Fit of the Balmer and helium lines in the co-added TWIN spectrum. The solid line shows the measurement, and the dashed line shows the best fitting synthetic spectrum.

7.4.4. The brown dwarf nature of the companion From the semi-amplitude of the radial velocity curve and the orbital period, we can derive the masses and the radii of both components for each mass ratio. To constrain the solutions further, we first compared the photometric surface gravity, which can be derived from the mass and the radius, to the spectroscopic surface gravity. This is displayed in Fig. 7.15. The spectroscopic surface gravity is consistent with the lightcurve solution for sdB masses from 0.25 to 0.6 M . It is, therefore, possible to find a self-consistent solution. This is not at all a matter of course, because gravity derived from photometry was found to be inconsistent with the spectroscopic result in other cases, such as AA Dor (Vuˇcković et al. 2008). We also compared the radius of the companion to theoretical mass-radius relations for low-mass stars and brown dwarfs with ages of 1, 5, and 10 Gyrs, respectively (Baraffe et al. 2003). As can be seen from Fig. 7.16, the measured mass-radius relation is well matched by theoretical predictions for stars & 3 Gyrs for companion masses between 0.055 M and 0.075 M . The corresponding mass range for the sdB star is from 0.39 M to 0.63 M , which is calculated from the mass ratio. However, the companion is exposed to intense radiation of a luminous hot star that is only 0.58 R away, which could lead to an underestimate of the radius, if compared to non-irradiated models (Baraffe et al. 2003). Such inflation effects have been found in the case of hot Jupiter exoplanets (e.g. Udalski et al. 2008) but also in the MS+BD binary CoRoT-15b (Bouchy et al. 2011). We can estimate the maximum inflation effect from theoretical mass-radius relations shown in Fig. 7.16. As can be seen from Fig. 7.16, inflation by more than 10% can be excluded because none of the theoretical mass-radius relations otherwise would match the measured one, even if the star was as old as 10 Gyrs (the age of the Galactic disk). If we assume an inflation of 5-10%, the mass-radius relation for the companion would be in perfect agreement with the light curve solution for a companion with a mass of 0.064 M and a radius of 0.085 R , and an age of ∼ 5-10 Gyrs. The corresponding mass of the sdB is close to the canonical sdB mass, which we therefore adopt for the sdB throughout the following discussion. As we calculated solutions for discrete q and, hence, discrete masses for the sdB and

87


0.475 M⊙

5

-2

log(g/cm s )

0.473 M⊙

B EH A T B EH A Z

5.5 0.471 M⊙

6 HeMS

40

35

30 Teff/1000 K

25

20

Figure 7.13.: Teff − log g diagram of the HW Vir systems. The solid lines are evolutionary tracks by Dorman et al. (1993) for an sdB mass of 0.471, 0.473, and 0.475 M . The positions of J1622 and J0820 are indicated with crosses. The other squares mark the position of other HW Vir-like systems (Van Grootel et al. 2013; Drechsel et al. 2001; For et al. 2010; Geier et al. 2011c; Maxted et al. 2002; Klepp & Rauch 2011; Østensen et al. 2008, 2010; Wood & Saffer 1999; Almeida et al. 2012; Barlow et al. 2013). The open dots represent other sdB binaries from the literature.

the companion, we adopted the solution closest to the canonical mass, which is also marked in Fig. 7.16. 7.4.5. Synchronisation Most HW Vir systems have orbital separations as small as one solar radius. Hence, it is reasonable to expect that the rotation of both components is tidally locked to the orbit. Indeed the rotation rates of HW Vir and other objects of the class with similarly short periods ( 0.1d) are found to be synchronised. It is worthwhile to note that the system PG 1017−036, a reflection-effect binary with almost the same parameters as J1622 (P = 0.072 d, K = 51 km s−1 , Teff = 30300 K, log g = 5.61), has a measured vrot sin i = 118 km s−1 (Maxted et al. 2002), which is fully consistent with synchronised rotation. However, J1622 (P = 0.0698 d, K = 47 km s−1 , Teff = 29000 K, log g = 5.65) rotates with vrot sin i = 71 km s−1 . With an inclination of 72.33◦ , this results in a rotational velocity of 74 km s−1 , which is only about two thirds of the rotational velocity expected for a synchronous rotation (Porbit = Prot = 2πR ). vrot The physical processes leading to synchronisation are not well understood in particular for stars with radiative envelopes, such as sdB stars and rivalling theories (Zahn 1977; Tassoul & Tassoul 1992)0.4 predict very different synchronisation timescales (for details see Geier et al. 2010). The synchronisation timescales increase strongly with orbital separation, hence with the orbital period of the system. Actually the objects J1622 and PG 1017−036 have the shortest periods and the highest probability for tidally locked rotation amongst all known HW Vir systems. Therefore, it is surprising that J1622 apparently is not synchronised, while PG 1017−036 is. Calculations in the case of the less efficient mechanism (Zahn 1977) predict that the synchronisation should be established after 105 yr, a time span much shorter than the EHB lifetime


Table 7.4.: Adopted lightcurve solution. Fixed parameters: q (= M2 /M1 ) Teff (1) g1b g2b x1 (B B)c x1 (R B)c δ2d

[K]

0.1325 29000 1.0 0.32 0.25 0.20 0.0

Adjusted parameters: [◦ ] [K]

72.33 ± 1.11 2500 ± 900 1.0 ± 0.03 0.9 ± 0.2 3.646 ± 0.17 2.359 ± 0.054 0.99996 ± 0.00077 0.99984 ± 0.00247 0.001 ± 0.003 1.0 ± 0.005 1.0 ± 0.005 0.0 0.045 ± 0.008

r1 (pole) r1 (point) r1 (side) r1 (back)

[a] [a] [a] [a]

0.284 ± 0.013 0.290 ± 0.015 0.290 ± 0.014 0.290 ± 0.014


[a] [a] [a] [a]

0.142 ± 0.009 0.150 ± 0.011 0.144 ± 0.009 0.149 ± 0.011

i Teff (2) Aa1 Aa2 Ωf1 Ωf2 L1 g L1 +L2 (BB ) L1 g L1 +L2 (BR ) δ1 x2 (BB ) x2 (RB ) l3 (BB )f l3 (RB )f Roche radiih :

a

Bolometric albedo Gravitational darkening exponent c Linear limb darkening coefficient; taken from Claret & Bloemen (2011) d Radiation pressure parameter, see Drechsel et al. (1995) e Fraction of third light at maximum f Roche potentials g Relative luminosity; L is not independently adjusted, but recomputed from r and T (2) 2 2 eff h Fractional Roche radii in units of separation of mass centres b

88

89


He I 4922

He I 4713

He I 4026

−10

−5

0 ∆λ[Å]

5

10

Figure 7.14.: Fit of the helium lines in the co-added ESI spectrum. The solid line shows the measurement and the dashed line shows the best fitting synthetic spectrum. The dotted line shows the line-broadening, if we assume synchronisation. 5.8 q=0.11 5.75 5.7

log g

5.65 5.6 5.55 q=0.19 5.5 5.45

canonical sdB mass

5.4 0

0.2

0.4 0.6 MsdB in M⊙

0.8

1

Figure 7.15.: Comparison of the photometric and spectroscopic surface gravity for the solutions with different mass ratio q = 0.11−0.19 (marked by the error cross). The spectroscopic surface gravity with uncertainty is given by the shaded area.

of 108 yr. Evidence for a non-synchronous rotation of sdB stars in reflection-effect binaries was presented recently by Pablo et al. (2011, 2012), who measured the rotational splittings of pulsation modes in three reflection-effect sdB binaries observed by the Kepler space mission, which reveals that the subdwarf primaries rotate more slowly than synchronised.


90

0.11 0.39 M⊙

0.47 M⊙

0.63 M⊙

Rcompanion [R⊙]

0.1 q=0.11

0.09

0.08

0.07

0.06 q=0.19 0.04

0.05

0.06 0.07 Mcompanion [M⊙]

0.08

0.09

Figure 7.16.: Comparison of theoretical mass-radius relations of brown dwarfs by Baraffe et al. (2003) for an age of 1 Gyr (filled triangles), 5 Gyrs (triangles) and 10 Gyrs (diamond) to results from the lightcure analysis. Each error cross represents a solution from the lightcurve analysis for a different mass ratio (q = 0.11 − 0.19). The dashed vertical lines mark different values of the corresponding sdB masses. The solid lines mark the solution closest to the canonical mass for the sdB star of 0.47 M that was adopted.

Table 7.5.: Parameters of J1622. SDSS J162256.66+473051.1 i

◦

MsdB Mcomp a RsdB Rcomp log g(sdB, phot) log g(sdB, spec)

[M ] [M ] [R ] [R ] [R ]

72.33 ± 1.11 0.48 ± 0.03 0.064 ± 0.004 0.58 ± 0.02 0.168 ± 0.007 0.085 ± 0.004 5.67 ± 0.02 5.65 ± 0.06

However, those binaries have rather long periods (∼ 0.5 d), and predicted synchronisation time scales are much longer than for J1622 and even exceed the EHB life time if the least efficient synchronisation process (see Fig. 19 in Geier et al. 2010) is adopted. Hence, unlike for J1622, the non-synchronisation of those systems is not in contradiction to synchronisation theory. It is quite unlikely that J1622 is too young for its rotation to be tidally locked to the orbit. Hence, we need to look for an alternative explanation. Tidal forces leading to circularisation and synchronisation may lead to stable configurations, in which the rotational and the orbital periods are in resonance; that is, their ratio is that of integer numbers as observed for Mercury. Comparing the observed rotational period of J1622 to the orbital one, we find that the ratio is 0.607 ± 0.065, hence close to a 2 to 3 resonance. However, J1622 must have undergone a spiral-in phase through the common-envelope phase and it must be investigated, whether such a resonant configuration can persist through that dynamical phase.

91


7.4.6. Conclusions We performed a spectroscopic and photometric analysis of the eclipsing hot subdwarf binary J1622, which was found in the course of the MUCHFUSS project. The atmospheric parameters of the primary are typical for an sdB star in a HW Vir system. Mass-radius relations were derived for both components. The mass of the sdB star is constrained from spectroscopy (surface gravity) to 0.28 M to 0.64 M . The mass of the companion can be constrained by theoretical mass-radius relations to lie between 0.055 M and 0.075 M , which implies that the sdB mass is between 0.39 M and 0.63 M . Assuming small corrections of about 5-10% to the radius due to the inflation of the companion by the strong irradiation from the primary, a companion mass of 0.064 M appears to be the most plausible choice that results in a mass of the sdB close to the canonical mass of 0.47M . Accordingly, the companion is a substellar object. This is the second time that a brown dwarf is found as a close companion to an sdB star. The object J1622 provides further evidence that substellar objects are able to eject a common envelope and form an sdB star. Finding more of these systems, helps to constrain theoretical models (Soker 1998; Nelemans & Tauris 1998). An important result of the spectral analysis is that the sdB star is rotating slower than expected, if its rotation was locked to its orbit, as observed for the very similar system PG 1017−036. The non-synchronous rotation of J1622 is in contradiction to the predictions of tidal interaction models unless the sdB star is very young. The ratio of the rotational to the orbital period is close to a resonance of 2 to 3. However, it has to be investigated further, if such a configuration can survive the common envelope phase. Future investigations should aim at the detection of spectral lines from the secondary to measure its radial velocity, which turns the system into an double-lined spectroscopic binary that would allow to pin down the mass ratio. Emission lines of the companion’s irradiated atmosphere have been detected in the sdOB system AA Dor (Vuˇcković et al. 2008) and also for the prototype HW Vir (Vuˇcković et al. 2014) most recently. Since J1622 is quite compact and the irradiation of the companion strong, such emission lines might be detectable in high-resolution spectra of sufficient quality. Accurate photometry is needed to confirm or disprove any asymmetries in its lightcurve, which hints at flows at the surface of the companion.


92

Table 7.6.: Radial velocities with errors of J1622. HJD

SDSS RV in km s−1

2452378.381481 2452378.398900 2452378.418200 2452378.442390

-107 -44 -18 -99

17 16 16 21

WHT 2455039.90179 2455068.90762 2455068.92338 2455068.94468 2455069.85954 2455069.92083 2455069.93150 2455070.85307 2455070.86036 2455070.86749 2455070.87733 2455070.88454 2455070.89174 2455071.93491 2455071.94215 2455071.94942 2455071.96599 2455071.96626 2455071.98042 2455071.99018 2455071.99739 2455072.01429 2455072.01457 2455072.02178

-64 -10 -22 -84 -79 -98 -100 -12 -5 8 -42 -79 -104 -73 -91 -78 -51 -17 0 -15 -23 -71 -100 -74

27 11 13 12 12 12 13 1 15 19 18 14 16 13 14 14 15 16 18 16 23 21 15 21

TWIN 2456073.37085 2456073.33931 2456073.38513 2456073.39285 2456073.40042 2456073.40799 2456073.41591 2456073.42347 2456073.43104 2456073.43950 2456073.44741 2456073.45546 2456073.45951 2456073.46356 2456073.46762 2456074.37223 2456074.37296 2456074.38264 2456074.38795 2456074.39366

26 -4 -62 -84 -72 -81 -71 -4 4 2 -41 -84 -85 -102 -81 -90 -116 -108 -104 -60

20 13 20 13 15 15 16 15 13 14 15 15 18 20 18 13 15 16 15 20

2456074.39883 2456074.40400 2456074.40918 2456074.41435 2456074.41952 2456074.42470 2456074.42987 2456074.43504 2456074.44022 2456074.44539 2456074.45057 2456074.45574 2456074.46091 2456074.46607 2456074.47125 2456074.47643 2456074.48159 2456075.47452 2456075.48320 2456075.49189 2456075.50058 2456075.51796 2456075.52665 2456075.53535 2456075.54404 2456076.53468 2456076.54337 2456076.55206 2456076.56075 2456076.56944 2456076.57813 2456077.35340 2456077.36210 2456077.37079 2456077.37948 2456077.52761 2456077.53631 2456077.55370 2456077.56240 2456077.57110 2456077.57980

-69 -59 -14 -26 -30 -33 -46 -78 -107 -129 -125 -91 -71 -55 -36 -46 -23 -60 -64 -92 -92 -15 9 -29 -45 -109 -89 -67 -42 -22 -11 -25 -99 -115 -92 -56 -32 -14 -4 -77 -97

20 16 14 18 15 13 13 18 16 17 14 19 15 17 16 18 15 18 15 17 20 18 20 19 23 13 15 20 20 13 17 13 20 18 16 20 15

-117 -109 -99 -79 -66 -53 -18 -14 -9 -12

10 10 11 11 11 12 12 11 12 11

17 20 18

ESI 2456121.76284 2456121.76704 2456121.77103 2456121.77522 2456121.77922 2456121.78318 2456121.78715 2456121.79114 2456121.79511 2456121.79910

93

7.5. TWO CANDIDATE BD COMPANIONS AROUND CORE HE-BURNING OBJECTS

7.5. Two candidate brown dwarf companions around core helium burning objects4 Here we report the discovery of a reflection effect, but no eclipses, in the light curves of two close sdB binaries. CPD-64◦ 481 and PHL 457 have been reported to be close sdB binaries with small RV shifts by Edelmann et al. (2005). Furthermore, PHL 457 has been identified as longperiod pulsator of V 1093 Her type (Blanchette et al. 2008). Those two sdBs are among the best studied close sdB binaries. Detailed analyses showed that both are normal sdB binaries with typical atmospheric parameters (CPD-64◦ 481: Teff = 27500 ± 500 K, log g = 5.60 ± 0.05 (Geier et al. 2010); PHL 457: Teff = 26500 ± 500 K, log g = 5.38 ± 0.05, (Geier et al. 2013a)). Geier et al. (2010) constrained the companion mass of CPD-64◦ 481 to be as high as 0.62 M by measuring the projected rotational velocity of the sdB and assuming synchronised rotation. This assumption is reasonable, as the theoretical synchronisation timescales with stellar mass companions due to tidal interactions for binaries with periods of about 0.3 d are much smaller or comparable to the lifetime of the sdB on the EHB, depending on the theory (see Geier et al. 2010). The inclination angle was predicted to be as small as 7◦ . Because no traces of the companion are seen in the spectrum, they concluded that the companion must be a WD, as main-sequence stars would be visible in the optical spectra, if their masses are higher than ∼ 0.45 M (Lisker et al. 2005). However, the detection of the reflection effect rules out such a compact companion. Using the same method we constrained the companion mass of PHL 457. Although the companion mass assuming synchronisation (∼ 0.26 M ) would still be consistent with observations, the derived inclination angle of 8◦ is very small and therefore unlikely. Moreover, observational evidence, both from asteroseismic studies (Pablo et al. 2011, 2012) and spectroscopic measurements (Schaffenroth et al. 2014c), indicates that synchronisation is not generally established in sdB binaries with low-mass companions (see also the discussion in Geier et al. (2010). Therefore, the rotation of the sdBs in CPD-64◦ 481 and PHL 457 is most likely not synchronised with their orbital motion and the method described in Geier et al. (2010) not applicable. 7.5.1. Time-resolved spectroscopy and orbital parameters In total, 45 spectra were taken with the FEROS spectrograph (R ' 48000, λ = 3800 − 9200 ˚ A) mounted at the ESO/MPG-2.2m telescope for studies of sdB stars at high resolution (Edelmann et al. 2005; Geier et al. 2010; Classen et al. 2011). The spectra were reduced with the FEROS pipeline available in the MIDAS package. The FEROS pipeline, moreover, performs the barycentric correction. To measure the RVs with high accuracy, we chose a set of sharp, unblended metal lines situated between 3600 ˚ A and 6600 ˚ A. Accurate rest wavelengths were taken from the NIST database. Gaussian and Lorentzian profiles were fitted using the SPAS (Hirsch Hirsch (2009)) and FITSB2 routines (Napiwotzki et al. 2004b, for details see Classen et al. (2011)). To check the wavelength calibration for systematic errors we used telluric features as well as night-sky emission lines. The FEROS instrument turned out to be very stable. Usually corrections of less than 0.5 km s−1 had to be applied. The RVs and formal 1σ-errors are given in Table 7.8 and 7.9. The orbital parameters and associated false-alarm probabilities are determined as described by Geier et al. (2011b). In order to estimate the significance of the orbital solutions and the contributions of systematic effects to the error budget, we normalised the χ2 of the most probable solution by adding systematic errors enorm in quadrature until the reduced χ2 reached ' 1.0. The hypothesis that both orbital periods are correct can be accepted with a high degree of 4

This chapter is based on Schaffenroth et al. (2014a)


94

Figure 7.17.: Radial velocity plotted against orbital phase. The RV data were phase folded with the most likely orbital periods. The residuals are plotted below.

confidence. The phased RV curves for the best solutions are of excellent quality (see Fig. 7.17). The derived orbital parameters are given in Table 7.7 and the orbital solution for CPD-64◦ 481 is perfectly consistent with the result presented in Edelmann et al. (2005). 7.5.2. Photometry Time-resolved differential photometry in BVR-filters for CPD-64◦ 481 and VR filters for PHL 457 was obtained with the SAAO STE4 CCD on the 1.0m telescope at the Sutherland site of the South African Astronomical Observatory (SAAO). Photometric reductions were performed us-

95


Table 7.7.: Derived orbital solutions, mass functions and minimum companion masses Object CPD-64◦ 481 PHL 457

T0a [−2 450 000]

Pa [d]

3431.5796 ± 0.0002 5501.5961 ± 0.0009

0.27726315 ± 0.00000008 0.3131 ± 0.0002

γa [km s−1 ]

Ka [km s−1 ]

93.54 ± 0.06 20.7 ± 0.2

23.81 ± 0.08 13.0 ± 0.2

enorm [km s−1 ]

f (M ) [M ]

M2b [M ]

icmax

0.16 0.7

0.0004 0.00007

> 0.048 > 0.027

70 75

a

The systematic error adopted to normalise the reduced χ2 (enorm ) is given for each case.

b

The minimum companion masses take into account the highest possible inclination.

c

i = 90 is defined as an edge-on orbit

◦

Table 7.8.: CPD-64◦ 481: All spectra were acquired with the FEROS instrument mid−HJD −2 450 000 3249.89041 3250.89408 3251.85033 3252.88158 3252.89956 3253.83281 3253.87777 3253.91205 3425.51834 3426.51685 3427.53343 3428.52983 3429.51370 3430.56510 3431.52045

RV [km s−1 ] 70.87 114.58 69.81 94.51 85.03 82.69 105.90 116.47 111.76 69.48 106.65 93.84 86.71 113.59 70.33

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.15 0.20 0.16 0.26 0.20 0.22 0.13 0.16 0.15 0.09 0.09 0.12 0.13 0.12 0.12

ing an automated version of DOPHOT (Schechter et al. 1993). The differential light curves have been phased to the orbital periods derived from the RV-curves and binned to achieve higher S/N. The light curves show sinusoidal variations (∼ 10 mmag) with orbital phase characteristic for a reflection effect (Fig. 7.18). It originates from the irradiation of a cool companion by the hot subdwarf primary. The projected area of the companion’s heated hemisphere changes while it orbits the primary. Compared to other reflection effect binaries the amplitude of the reflection effect in both systems is quite small. The amplitude of the reflection effect depends mostly on the separation of the system, the effective temperature of the subdwarf, and the visible irradiated area of the companion. Seen edge-on, the relative change of this area is the highest. However, for small inclinations the derived mass of the companion becomes higher and because there is a strong correlation between mass and radius on the lower main sequence (see Fig. 7.19), the radius of the companion and the absolute irradiated area becomes larger as well. Due to this degeneracy it is therefore not straight forward to claim that small reflection effects can simply be explained by small inclination angles. We fitted models calculated with MORO, which is based on the Wilson-Devinney code (MOdified ROche model, Drechsel et al. (1995)), to the light curves as described in (Schaffenroth et al. 2013). As no eclipses are present, the inclination is difficult to determine and we fitted light curve solutions for different fixed inclinations. The mass ratio, which can be calculated from the mass function for different inclinations, was also kept fixed, so that the mass of the sdB


96

Table 7.9.: PHL 457: All spectra were acquired with the FEROS instrument mid−HJD −2 450 000 3249.64149 3250.64322 3251.58746 3253.56948 5500.52235 5500.54504 5501.52731 5501.53727 5501.54722 5501.55718 5501.56712 5501.57705 5501.58698 5501.59692 5501.60685 5502.50148 5502.51028 5502.51908 5502.52785 5502.53663 5502.54542 5502.55420 5502.56298 5502.57175 5502.58053 5502.58932 5502.59811 5502.60688 5502.61566 5502.62502

RV [km s−1 ] 10.1 22.2 23.8 29.4 15.1 9.7 8.4 9.1 9.3 11.0 14.1 16.4 17.2 21.1 22.2 13.0 13.9 16.1 18.5 21.8 23.4 24.3 28.4 30.9 31.0 31.3 33.2 34.8 34.1 32.7

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.2 0.2 0.3 0.3 0.2 0.5 0.2 0.3 0.2 0.1 0.2 0.2 0.2 0.3 0.8 0.4 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.3

is equal to the canonical sdB mass MsdB = 0.47 M (see Fontaine et al. 2012, and references therein). Shape and amplitude of the variation mostly depends on the orbital inclination and the mass ratio, but also on the radius ratio of both components and the unknown albedo of the companion. Due to this high number of parameters, that are not independent from each other, we cannot find a unique solution. Selecting only solutions for which the photometric radius is consistent with the spectroscopic radius derived from the surface gravity, we narrow down the number of solutions. Unfortunately, due to the degeneracy between the binary inclination and the radius of the companion we find equally good solutions for each inclination (see also Østensen et al. 2013). In the case of CPD64◦ 481, see Fig. 7.19, the derived mass and radius of the companion are in agreement with theoretical relations by Chabrier & Baraffe (1997) for the entire range of inclinations. In the case of PHL 457 the theoretical mass-radius relation is only consistent for an inclination of 5070◦ . For lower inclinations the measured radius would be larger than expected by the models. However, due to the many assumptions used in the analysis, it is difficult to estimate the significance of this result, as a smaller mass for the sdB could solve this issue.

97


CPD -64 481 1 0.995

B

relative flux

0.99 0.985

V

0.98 0.975

R

0.97 0.965 0.96

0.955 -0.4

-0.2

0

0.2

0.4

0.6

0.4

0.6

phase PHL 457 1 0.995 relative flux

0.99

V

0.985 0.98

R

0.975 0.97 0.965 0.96 -0.4

-0.2

0

0.2 phase

Figure 7.18.: Phased and binned light curves in B-, V- and R-bands in the case of CPD-64◦ 481 (upper panel) and V- and R-bands in the case of PHL 457 (lower panel). Overplotted are two models for an inclination of 10◦ (solid) and 65◦ (dashed) for CPD-64◦ 481 and 10◦ (solid) and 70◦ (dashed) for PHL 457. The lightcurve models with higher inclinations (dashed) have broader minima and shallower maxima.

In Fig. 7.18 we show model light curves for high and low inclination. Although small differences are present, a much better quality light curve is required to resolve them. The sum of the deviations between the measurements and the models are somewhat, but not significantly, smaller for low inclinations. Therefore, we cannot draw firm conclusions from our photometric data at hand.


98

0.4 i=10 0.35

Rcompanion [R⊙]

0.3 0.25 0.2 0.15 i=65 0.1 0.05 0 0

0.05

0.1

0.15

0.2 0.25 0.3 Mcompanion [M⊙]

0.35

0.4

0.45

0.5

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Mcompanion [M⊙]

0.2

0.3

Rcompanion [R⊙]

0.25

i=10

0.2

0.15 i=70 0.1

0.05 0

Figure 7.19.: Mass-radius relation of the companion of CPD-64◦ 481 (upper panel) and PHL 457 (lower panel) for different inclinations (filled rectangles), compared to theoretical relations by Chabrier & Baraffe (1997) for an age of the system of 1Gyr (short dashed line), 5 Gyr (long dashed line) and 10 Gyr (solid line). For all shown solutions mass and radius of the sdB are also consistent with the spectroscopic surface gravity measurement of log g = 5.60 ± 0.05 for CPD-64◦ 481 (Geier et al. 2010) and log g = 5.38 ± 0.05 (Geier et al. 2013a) for PHL 457.

7.5.3. Brown dwarf nature of the unseen companions 3 The two binaries are single-lined and their binary mass functions fm = Mcomp sin3 i/(Mcomp + MsdB )2 = P K 3 /2πG can be determined. The RV semi-amplitude and the orbital period can be derived from the RV curve, but the sdB mass MsdB , the companion mass Mcomp and the inclination angle i remain free parameters. Adopting the canonical sdB mass MsdB = 0.47 M and the imax , that can be constrained, because no eclipses are present in the lightcurve, we

99


derive lower limits for the companion masses (see Table 7.7). Those minimum masses of 0.048 M for CPD-64◦ 481 and 0.027 M for PHL 457 - the smallest minimum companion mass measured in any sdB binary so far - are significantly below the hydrogen-burning limit (∼ 0.07 − 0.08 M , Chabrier et al. (2000)). As no features of the companion are found in the spectrum, we also derive an upper mass limit of ∼ 0.45 M (Lisker et al. 2005) . The initial sample of Edelmann et al. (2005) consisted of known, bright hot subdwarf stars. Because no additional selection criteria were applied, it can be assumed that the inclination angles of the binaries found in this survey are randomly distributed. Due to the projection effect it is much more likely to find binary systems at high rather than low inclinations. The probability, that a binary has an inclination higher than a certain angle, can be calculated as described in Gray (2005), Pi>i0 = 1 − (1 − cos i0 ) . Since the companion mass scales with the inclination angle, we can derive the probability that the mass of the companion is smaller than the hydrogen-burning limit of ∼ 0.08 M , which separates stars from brown dwarfs. For CPD-64◦ 481, the inclination angle must be higher than 38◦ , which translates into a probability of 79%. In the case of PHL 457, an inclination higher than 21◦ is required and the probability for the companion to be a brown dwarf is as high as 94%. We therefore conclude that the cool companions in those two binary systems are likely brown dwarfs. The only chance to constrain the inclination better would be very high signal-to-noise lightcurves. Moreover, high resolution, high S/N spectra could help to constrain the mass ratio of the system. They could allow to discover emission lines from the irradiated hemisphere of the companion, as done for the sdOB+dM system AA Dor (Vuˇcković et al. 2008). The strength of the emission lines should be independent of the inclination, depending only on the size of the companion, the separation of the system and the effective temperature of the primary. As the systems are very bright, it might be possible to find these emission lines despite the larger separation and lower effective temperature of our systems. 7.5.4. Discussion Figure 7.20 gives an overview of the 29 sdB binaries with reflection effect and known orbital parameters (Kupfer et al. 2015). While most companions are late M-dwarfs with masses close to ∼ 0.1 M , there is no sharp drop below the hydrogen-burning limit. The fraction of close substellar companions is substantial. An obvious feature in Fig. 7.20 is the lack of binaries with periods shorter than ∼ 0.2 d and K < 50 km s−1 corresponding to companion masses of less than ∼ 0.06 M . This feature could not be due to selection effects. About half of the known reflection effect binaries have been found based on RV-shifts detected in time-resolved spectra. As has been shown in this work, RV-semiamplitudes of a few tens of km s−1 are easily measurable. Furthermore, short-period binaries are found and solved easier than long-period systems. The other half of the sample has been discovered based on variations in their light curves. Shape and amplitude of the light curves depend mostly on the radius of the companion for similar orbital periods and separations. Since the radii of late M-dwarfs, brown dwarfs and also Jupiter-size planets are very similar (∼ 0.1 R ), their light curves are expected to be very similar as well. The most likely reason for this gap is the merger or evaporation of low-mass companions either before or after the CE-ejection corresponding to a population of single sdB stars. Other recent discoveries are perfectly consistent with this scenario. Charpinet et al. (2011) reported the discovery of two Earth-sized bodies orbiting a single pulsating sdB within a few hours. These might be the remnants of a more massive companion evaporated in the CE-phase (Bear & Soker 2012). Geier et al. (2011b, 2013b)) found two fast rotating single sdBs, which might have formed in a CE-merger. Those discoveries provide further evidence that substellar companions


100

Figure 7.20.: The RV semiamplitudes of all known sdB binaries with reflection effects and spectroscopic solutions plotted against their orbital periods (Kupfer et al. 2015). Diamonds mark eclipsing sdB binaries of HW Vir type where the companion mass is well constrained, triangles systems without eclipses, where only lower limit can be derived for the companion masses. Squares mark CPD-64◦ 481, PHL 457, KBS 13 and BPS CS 22169−0001. Open symbols mark systems that have been discovered based on photometry, filled symbols have been discovered based on spectroscopy. The dashed lines mark the regions to the right where the minimum companion masses derived from the binary mass function (assuming 0.47 M for the sdBs) exceed 0.01 M (lower curve) and 0.08 M (upper curve).

play an important role in the formation of close binary and likely also single sdB stars. We therefore conclude that the lack of short period systems with small RV variations K < 50 km s−1 is real. However, the probability that substellar companions are present in systems with longer periods (> 0.2 d) is quite high. In addition to the two binaries discussed here, two more systems with similar orbital parameters and reflection effects have been found (KBS 13, For et al. (2008); BPS CS 22169−0001, Geier & Heber (2012)). Following the line of arguments outlined above, we calculate the probability for those two systems to host a stellar companion to be 9% for BPS CS 22169−0001 and 20% for KBS 13. Multiplying those numbers for all four binaries, we conclude that the probability that none of them has a substellar companions is less than 0.02%.

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7.6. AN ECLIPSING BINARY WITH A PULSATING SDB AND A BD COMPANION

7.6. An eclipsing post common-envelope system consisting of a pulsating hot subdwarf B star and a brown dwarf companion5 Van Noord et al. (2013) reported the discovery of a promising new HW Virginis system, V20081753 (CV=16.8 mag), which was found during an automatic search for variable stars conducted with the 0.4 m Calvin College Robotic Telescope in Rehoboth, New Mexico. Their relatively noisy light curve showed eclipses and a strong reflection effect. Interestingly, this sdB binary has an orbital period of only 1.58 h, the shortest period ever found in an HW Virginis system. Here we present the first thorough analysis of this unique system, along with the discovery of low–amplitude pulsations in the sdB primary. Section 7.6.1 describes the observational data. The analysis is discussed in Sects. 7.6.2 (spectroscopy) and 7.6.3 (photometry). Evidence for the brown dwarf nature of the companion is discussed in Sect. 7.6.4. Finally, we end with conclusions and suggest further opportunities that are offered by this one-of-a-kind system. 7.6.1. Observations Time–series spectroscopy

We used the Goodman Spectrograph on the 4.1–m SOuthern Astrophysical Research (SOAR) telescope to obtain time–series spectroscopy of V2008-1753 over a full orbital cycle and determine the orbital velocity of its primary sdB component. A 1.35” longslit and a 930 mm−1 VPH grating from Syzygy Optics, LLC, were employed to cover the spectral range 3600–5250 ˚ A with an approximate resolution of 3.8 ˚ A (0.84 ˚ A per binned pixel). The position angle was set to 197.8 degrees E of N so that we could place a nearby comparison star on the slit, with the intention of characterizing and removing instrumental flexure effects. In order to maximize our duty cycle, we binned the spectral images by two in both the spatial and dispersion directions and read out only a 2071 x 550 (binned pixels) subsection of the chip. Each exposure had an integration time of 90 s, with 8 s of overhead between successive images, yielding a duty cycle of approximately 92%. Overall, we acquired 70 spectra of V2008-1753 between 23:49:20.87 UT (2013-08-31) and 01:42:07.17 UT (2013-09-01). The airmass decreased from 1.22 to 1.03 over this time period. Upon completion of the time series, we obtained several FeAr comparison lamp spectra and quartz–lamp spectra for wavelength calibration and flat–fielding. Standard routines in IRAF, primarily ccdproc, were used to bias–subtract and flat–field the spectral images. Given the low thermal noise in the spectrograph system, we did not subtract any dark frames, as we wanted to avoid adding noise to the images. We used apall to optimally extract one–dimensional spectra and subtract a fit to the sky background for both the target and constant comparison star. Finally, we wavelength–calibrated each spectrum using the master FeAr comparison lamp spectrum taken at the end of the time–series run. The resulting individual spectra of V2008-1753 had a signal–to–noise ratio (S/N) around 15–20 pixel−1 , while the individual spectra of the comparison star (which looked to be G or K–type), had a S/N twice as high. Time–series photometry

High–precision photometry was acquired with SOAR/Goodman through i’ and g’ filters on 15/16 August 2013. Although our primary goal was to model the binary light curve, our secondary goal was to look for stellar pulsations, and thus we used an instrumental setup that had both a high duty cycle and a Nyquist frequency above those of most known sdB pulsation modes. We binned the images 2 x 2 and read out only a small 410 x 540 (binned pixel) subsection of the chip that included both the target and 10 comparisons stars with the same 5

This chapter is heavily based on Schaffenroth et al. (2015)


102

80

radial velocity [km s-1]

60 40 20 0 -20 -40 -60 -80

residuals

40 20 0 -20 -40 0

0.25

0.5

0.75 1 1.25 orbital phase

1.5

1.75

2

Figure 7.21.: Top panel: Radial velocity curve for the sdB primary in V2008-1753, plotted twice for better visualization. The solid line denotes the best–fitting circular orbit to the data. Bottom panel: Residuals after subtracting the best–fitting sine wave from the data.

approximate brightness level. We achieved an 87% duty cycle with 25-s exposures for the g’ light curve and a 81.4% duty cycle with 14-s exposures for the i’ light curve. In both cases, we observed the field for at least one full orbital cycle near an airmass of 1.1. We concluded each night with a set of bias frames and dome flats. Thermal count rates were too low to warrant the acquisition of dark frames. All object images were bias–subtracted and flat–fielded using IRAF’s ccdproc package. We extracted light curves with an IDL program we wrote that uses the function APER, which is based on DAOPHOT (Stetson 1987). We produced light curves over a wide range of aperture radii and selected the aperture that maximized the S/N in the light curve. To mitigate the effects of atmospheric extinction and transparency variations, we divided the light curve of V2008-1753 by the average of those of the constant comparison stars, after verifying they were indeed non–variable. Residual extinction effects are often removed in light curves of this duration by fitting and dividing the light curve by the best-fitting parabola. However, given the large-amplitude binary signals present, this process would distort the actual stellar signal, Instead, we fit straight lines through points of the same phase and, informed by these fits, removed the overall ’tilt’ in each light curve. While not perfect, this process helps to mollify the effects of residual extinction variations. We then divided each light curve by its mean value and subtracted a value of one from all points to put them in terms of fractional amplitude variations.

103


7.6.2. Spectroscopic analysis Radial velocity curve

Radial velocity shifts were determined by measuring the positions of the hydrogen Balmer profiles Hβ through H9; although H10, H11, and several He I lines were also present, they were too noisy to provide reliable positions. We used the MPFIT routine in IDL (Markwardt 2009), which relies on the Levenberg-Marquardt method, to fit simple inverse Gaussians to the line profiles and determine their centroids. The only available guide star near our field was significantly redder than the sdB target, and, consequently, its use led to a gradual shift in the slit alignment over the course of our observations (the Goodman spectrograph had no atmospheric dispersion corrector at the time); this drifting results in a color–dependent velocity shift. Additionally, instrumental flexure as the Nasmyth cage rotates also affected the stars’ alignment on the slit, although only slightly. We removed both of these time–dependent wavelength solution effects by tracking the absorption–line features in the constant comparison star. Figure 7.21 presents the resulting radial velocity curve for V2008-1753, plotted twice for better visualization We again used MPFIT to fit a sine wave to the data and determine the semi–amplitude of the velocity variation; the orbital period and phase were fixed during this process. We derive an orbital velocity of K = 54.6 ± 2.4 km s−1 for the sdB primary. Eccentric orbits were also fitted to the radial velocity curve, but as we currently have no reason to prefer them over e = 0, we continue the analysis under the assumption that the orbit is circular. Residuals from the best–fitting sine wave are shown in the bottom panel of Figure 7.21 and are consistent with noise. The mean noise level in the Fourier transform of the residual velocity curve is 2 km s−1 . Atmospheric parameters

In preparation for determining the atmospheric parameters of the sdB, we first de–shifted all individual spectra according to our orbital solution above and then co–added them to improve the overall S/N. We fit synthetic spectra, which were calculated using local thermodynamical equilibrium model atmospheres with solar metallicity and metal line blanketing (Heber et al. 2000), to the Balmer and helium lines of the co-added SOAR spectrum using SPAS (SPectral Analysis Software, Hirsch 2009). The best–fitting synthetic spectrum had the following orbital parameters: Teff = 32800 ± 250 log g = 5.83 ± 0.04 log y = −2.27 ± 0.13 with 1-σ statistical errors determined by bootstrapping. For some sdB systems with reflection effects, an analysis of spectra with sufficiently high S/N taken at different phases shows that the atmospheric parameters apparently vary with phase (e.g. Schaffenroth et al. 2013, 2014c). These variations can be explained by the companion’s contribution to the spectrum (reflection only) varying with orbital phase. Systems with similar parameters show such variations in temperature and surface gravity on the order of 1000 − 1500 K and 0.1 dex, respectively. To account for the apparent change in the parameters we formally adopt the values determined from the co-added spectrum, which represents a mean value, with a larger error: Teff = 32800 ± 750 K and log g = 5.83 ± 0.05 for the sdB. Figure 7.22 shows the corresponding fit of the Balmer and helium lines. We excluded H from the fit, as this line is mostly blended with the Ca II H-line and hence is less well represented by this fit. The Teff −log g diagram is displayed in Fig. 7.23 and shows that V2008-1753 lies in the middle of the extreme horizontal branch. Although it was previously suggested that HW Virginis systems


104

He I 4922 He I 4472 He I 4026


−30

−20

−10

0 ∆λ[Å]

10

20

30

Figure 7.22.: Fit of the Balmer and helium lines in the co-added SOAR spectrum. The solid line shows the measurement, and the dashed line shows the best fitting synthetic spectrum. As the H seems to be effected by a blend of the Ca line next to it, it was excluded from the fit.

cluster together only in a small part of the Teff − log g diagram (Schaffenroth et al. 2014c), the position of V2008–1753 seems to go against this hypothesis. However, it is still apparent that most of the known HW Vir systems and reflection effect binaries (both sdB+dM systems with different inclinations) concentrate in a distinct region between a Teff of 26000-30000 K and a log g of about 5.3 to 5.7, only at the edge of the instability strip. There are five exceptions of binaries with sdOB star primaries and M star companions at higher temperatures, which are possibly just more evolved. Yet, the three HW Vir systems showing short-period p-mode pulsations with amplitudes observable from the ground lie in a different part of the Teff − log g diagram, nearer to the He-MS, in the central part of the instability strip for sdBVr s, as expected. In contrast to that the other sdB binaries with either white dwarf secondaries or companions of unknown type do not show any clustering but are uniformly distributed over the EHB. This could indicate that the sdBs with low-mass main-sequence companions differ from the sdBs with white dwarf companions.

105


0.475 M⊙

5 0.473 M⊙

HB E A

T

log(g/cm s-2)

B

EH A Z

5.5 0.471 M⊙

6

sdBV instability strip HeMS

40

35

30 Teff/1000 K

25

20

Figure 7.23.: Teff − log g diagram of the HW Vir systems. The helium main sequence (HeMS) and the EHB band (limited by the zero-age EHB, ZAEHB, and the terminal-age EHB, TAEHB) are superimposed by evolutionary tracks by Dorman et al. (1993) for sdB masses of 0.471, 0.473, and 0.475 M . The positions of the HW Vir systems with pulsating sdBs – V2008-1753 (this work, with error bars), NY Vir (Van Grootel et al. 2013), 2M1938+4603 (Østensen et al. 2010), and PTF1 J072456+125301 (Schindewolf et al. submitted, Kupfer priv. com.) – are marked by red squares. Blue dots mark the positions of other HW Virlike systems (Drechsel et al. 2001; For et al. 2010; Maxted et al. 2002; Klepp & Rauch 2011; Østensen et al. 2008; Wood & Saffer 1999; Almeida et al. 2012; Barlow et al. 2013; Schaffenroth et al. 2013, 2014b, Schaffenroth et al., in prep, Kupfer, priv. com.). The positions of the two HW Vir systems with BD companions J1622 (Schaffenroth et al. 2014c) and J0820 (Geier et al. 2011c) are indicated by the blue dots with error bars. The black triangles mark sdB+dM systems showing a reflection effect but no eclipses (Kupfer et al. 2015, and references therein). The green, open dots represent other sdB+WD binaries or sdB binaries with unknown companion type (Kupfer et al. 2015). The approximate location of the sdBVr instability strip is indicated by an ellipse.


106

Table 7.10.: Pulsation frequencies and amplitudes f a,b [mHz]

amplitude [ppt]

F1 F2 F3 F4

6.565±0.005 5.494±0.008 6.289±0.006 5.638±0.011

3.5± 3.1± 3.1± 2.2±

0.2 0.2 0.2 0.2

F1 F2 F3 F4

6.572±0.006 – 6.295±0.006 5.685±0.008

3.2± 0.3 – 2.8± 0.3 2.3± 0.3

phasec

S/N

0.739±0.019 0.82±0.03 0.74±0.02 0.71±0.05

14.5 12.6 12.5 9.2

0.12±0.03 – 0.90±0.04 0.87±0.03

8.7 – 7.6 6.2

a

upper half: frequencies found in g’ light curve lower half: frequencies found in i’ light curve b errors as given by FAMIAS, more realistic is an error around 0.1-0.2 mHz c reference time: first point of light curve (g’: BJDTBD = 2456519.5846905) (i’: BJDTBD = 2456520.53415896)

7.6.3. Photometric analysis

Pulsations

Both the g’ and i’ light curves from the SOAR telescope exhibit pulsations too low in amplitude to have been detected in the data analysed by Van Noord et al. (2013). In order to disentangle the pulsations from the binary effects in the light curve, we used an approach similar to that demonstrated by Vuˇcković et al. (2007). First, we fit the eclipses and reflection effect as described in Section 7.6.3) and subtracted the best-fitting model from the observed light curve. The original g’ and i’ filter light curves are displayed in Fig. 7.24, along with the same curves after the subtraction of the binary signal. The pulsations are visible by eye in the g’ curve but less apparent in the i’ data, due to its lower S/N and lower pulsation amplitudes at redder wavelengths. The large–scale trends in both residual light curves are likely due to residual atmospheric extinction and transparency variations. We calculated the Fourier transformations (FTs) of the light curves using FAMIAS6 (Zima 2008). The resulting FTs are displayed in Fig. 7.25. We detect at least four independent pulsation modes with periods ranging from 2.5 to 3 min and amplitudes < 4 ppt. The best–fit frequencies, along with their amplitudes and S/N, are listed in Table 7.10. The mode with the second–highest amplitude in the g’ light curve (F2) was not clearly detected in the i’ light curve, but its apparent absence might be explained by the high noise level in this data set. The elevated power at lower frequencies is likely due to inaccuracies in the binary light curve modeling, along with the atmospheric extinction and transparency corrections. A much longer time base is needed to improve the frequency determination and to be able to use the pulsations for asteroseismology. Consequently, we do not perform a more thorough pulsation analysis than this and limit our result simply to the detection of pulsations alone. To prepare the light curve for binary modeling, we use the results from Table 7.10 to subtract the detected pulsations from the original light curves.


rel. flux

107

0 -0.05 g’

normalized flux

1

0.8 i’ 0.6

0.4 0

2000

4000

6000 time [s]

8000

10000

Figure 7.24.: g’ (dashed line) and i’ (solid line) filter light curves of V2008-1753 taken with SOAR. The two light curves were taken in subsequent orbital cycles. The sub-figure shows the pulsation signal after the subtraction of the binary signal by the best-fitting light curve model. Binary Light Curve Modeling

The binary light curve exhibits all the typical features of a HW Vir system. Due to the short period and the relatively high temperature of the subdwarf, the reflection effect is rather strong, with an amplitude around 10 %. The secondary eclipse appears to be nearly total, in accordance with the high inclination and the very deep primary eclipse. As our light curves only cover one complete orbital cycle, it is not possible to determine an accurate period from our data alone. For the ephemeris we hence cite the period derived by Van Noord et al. (2013), which was determined from a much larger baseline. We were able to determine precise eclipse timings using our data by fitting parabolas to the minima. They are summarized in Table 7.11. Using these values and the period from Van Noord et al. (2013), the ephemeris of the primary minimum is given by BJDTBD = 2456519.64027(1) + 0.065817833(83) · E

(7.3)

where E is the cycle number. The error in the period quoted by Van Noord et al. (2013) is likely to be an underestimate given the omission of systematics and the poor sampling. We believe an error of 0.0001 to be more appropriate. A comparison of the secondary eclipse compared to the primary eclipse of both light curves separately reveals a slight departure of the secondary mid-eclipse from phase 0.5; such an offset can be caused by both the Rømer delay (extra light travel time due to the binary orbit) and an eccentricity e > 0. For small eccentricities, the total shift of the secondary eclipse with respect to phase 0.5 is given in Barlow et al. (2012a): P KsdB 1 2P ∆tSE w ∆tRømer + ∆tecc w −1 + e cos ω πc q π From both light curves we measure a shift of 3±1 s between the time of the secondary minimum and phase 0.5. With our system parameters we would expect a theoretical shift of the secondary 6

http://www.ster.kuleuven.be/~zima/famias


0.004

108

0.003

0.0035

0.0025

0.002

0.0025

amplitude

amplitude

0.003

0.002 0.0015

0.0015

0.001

0.001 0.0005

0.0005 0

0 0

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 frequency [Hz]

0

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 frequency [Hz]

Figure 7.25.: Fourier transform of the pulsation signal shown in the sub-figure of Fig. 7.24. The right and left figures show the FTs of the g’ and the i’ filter light curves, respectively.

Table 7.11.: Eclipse times filter

eclipse

BJDTBD [d]

g’ g’ i’ i’ i’

primary secondary primary secondary primary

2456519.64027(1) 2456519.60733(2) 2456520.56176(1) 2456520.59463(1) 2456520.62757(1)

eclipse with respect to phase 0.5 due to the Rømer delay of 2 s. If we take that into account, we would get a maximal eccentricity of e · cos ω < 0.00055. Ignoring the Rømer delay results in a maximum eccentricity of e · cos ω < 0.0011. Because of the large errors in the radial velocity determinations, the eccentricity cannot be constrained by the radial velocity curve to that precision. A photometric solution to the binary light curve (with pulsations removed; Fig. 7.26) was determined using MORO (MOdified ROche program, see Drechsel et al. 1995). This program calculates synthetic light curves which we fit to the observations using the SIMPLEX algorithm. This light curve solution code is based on the Wilson-Devinney approach (Wilson & Devinney 1971) but uses a modified Roche model that considers the mutual irradiation of hot components in close binary systems. More details of the analysis method are described in Schaffenroth et al. (2013). To calculate the synthetic light curves, 12 + 5n (n is the number of light curves) parameters are used. Such a high number of partially–correlated parameters will inevitably cause severe problems if too many and wrong combinations are adjusted simultaneously. In particular, there is a strong degeneracy with respect to the mass ratio. After the orbital inclination, this parameter has the strongest effect on the light curve, and it is highly correlated with the component radii. Hence we kept the mass ratio fixed at certain values and calculated solutions for these mass ratios, which were subsequently compared and evaluated according to criteria explained below. Given the large number of parameters present in the code, it is imperative to constrain as many parameters as possible based on independent inputs from spectroscopic analyses or theoretical constraints. From the spectroscopic analysis, we derived the effective temperature and the surface gravity of the sdB primary and fixed these parameters during the fitting. Due to the early spectral type of the primary star, the gravity darkening exponent was fixed at g1 = 1, as expected for radiative outer envelopes (von Zeipel 1924). For the cool convective companion,

109


1.2 1.1

g’

normalized light

1 i’ 0.9 0.8 0.7

residuals residuals

0.6 0.5 0.01 0 -0.01 0.02 0 -0.02 0.4

0.6

0.8

1 1.2 orbital phase

1.4

1.6

Figure 7.26.: g’ and i’ light curves after the removal of the pulsation signal as explained in Sect. 7.6.3 together with the best-fitting light curve model. The residuals displayed in the two lower panels still show signs of low-amplitude pulsations.

g2 was set to 0.32 (Lucy 1967). The linear limb darkening coefficients were extrapolated from the table of Claret & Bloemen (2011). To determine the quality of the light curve fit, the sum of squared residuals σ of all observational points with respect to the synthetic curve was calculated as a measure of the goodness of the fit. Unfortunately, the σ values of the best light curve fits for the different mass-ratios did not differ significantly. Therefore, we cannot determine a unique solution from the light curve analysis alone. The full set of parameters describing the best–fitting solution for a mass ratio of q = 0.146, which corresponds to an sdB with the canonical mass of 0.47 M are given in Table 7.13, with errors determined by the bootstrapping method. The light curves in the g 0 and i0 bands are displayed in Fig. 7.26 together with the best-fit models for these parameters. The parameters of the system derived from this lightcurve solution together with the semiamplitude of the RV curve are summarized in Table 7.12. The errors result from propagation of the uncertainties in K and P .

7.6.4. The brown dwarf nature of the companion From the semi-amplitude of the radial velocity curve, the orbital period, and the inclination, we can derive the masses and radii of both components for each mass ratio. The masses follow


110

Table 7.12.: Parameters of V2008-1753 coordinates cv i K P MsdB Mcomp a RsdB Rcomp log g(sdB, phot) log g(sdB, spec) Teff,sdB

V2008-1753 20 08 16.355 -17 53 10.52 (J2000.0) [mag] 16.8 ◦

[km s−1 ] [h] [M ] [M ] [R ] [R ] [R ]

[K]

86.83 ± 0.45 54.6 ± 2.4 1.5796280 ± 0.0000002 0.47 ± 0.03 0.069 ± 0.005 0.56 ± 0.02 0.138 ± 0.006 0.086 ± 0.004 5.83 ± 0.02 5.83 ± 0.05 32800 ± 750

from: P K13 (q + 1)2 2πG (q · sin i)3 M2 = q · M1

M1 =

and the fractional radii of the light curve solution together with P K1 1 a= · +1 2π sin i q

yield the radii. For each mass ratio we get different masses and radii. It was stated already in Sect. 7.6.3 that it is not possible to determine the mass ratio from the light curve analysis alone. However, from the sdB mass and radius determined by the light curve analysis we can calculate a photometric surface gravity and compare that to the surface gravity derived by the spectroscopic analysis. The result is shown in Fig. 7.27. An agreement of spectroscopic and photometric surface gravity values is reached for solutions that result in sdB masses between 0.35 and 0.62 M . It is therefore possible to find a self-consistent solution. This is a fortunate situation, because gravity derived from photometry was found to be inconsistent with the spectroscopic result in other cases, such as AA Dor (Vuˇcković et al. 2008). To constrain the solutions even more, we can also use theoretical mass-radius relations for the low-mass companions by Baraffe et al. (2003) and compare them to the masses and radii of the companion derived by the light curve solutions for the various mass ratios. This was done in a similar way as in Schaffenroth et al. (2014c). This comparison is displayed in Fig. 7.28. Relations for different ages of 1, 5 and 10 Gyrs were used. The measured mass-radius relation is well matched by theoretical predictions for stars & 3 Gyrs for companion masses between 0.056 M and 0.073 M . The corresponding mass range for the sdB star extends from 0.35 M to 0.53 M . However, inflation effects have been found in the case of hot Jupiter exoplanets (e.g. Udalski et al. 2008) and also in the MS + BD binary CoRoT-15b (Bouchy et al. 2011). As the companion is exposed to intense radiation of a luminous hot star at a distance of only 0.56 R , this effect

111


6 5.95

q=0.10

log g

5.9 5.85 5.8 5.75

canonical sdB mass q=0.19

5.7 0

0.2

0.4

0.6 0.8 MsdB [M⊙]

1

1.2

1.4

Figure 7.27.: Comparison of the photometric and spectroscopic surface gravity for the solutions with different mass ratio q = 0.10−0.19 (marked by the error cross). The spectroscopic surface gravity with uncertainty is given by the shaded area.

cannot be neglected and would result in an underestimation of the radius, if compared to nonirradiated models (Baraffe et al. 2003). The maximum inflation effect can be estimated from the comparison of our solutions to the theoretical mass-radius relations shown in Fig. 7.28. This figure shows that an inflation of more than about 10 % can be excluded, because otherwise none of the theoretical mass-radius relations would match the measured one, even if the star were as old as 10 Gyrs. The mass-radius relation for the companion would be in perfect agreement with the light curve solution for a companion with a mass of 0.069 M , a radius of 0.086 R , and an age of ∼ 510 Gyrs, if we assume an inflation of 6-11 %. The corresponding mass of the sdB is 0.47 M , exactly the canonical sdB mass, which we therefore adopt for the sdB throughout the rest of this section. A similar result was found in the analysis of the sdB + BD binary J1622 (Schaffenroth et al. 2014c), which has a comparable period and parameters. The companion has a mass below the limit for hydrogen-burning and thus appears to be a brown dwarf – the third confirmed around a hot subdwarf star. 7.6.5. Summary and conclusions We performed an analysis of the spectrum and light curve of V2008-1753 and find that this eclipsing binary consists of a pulsating sdB with a brown dwarf companion. This is the first system of this kind ever found. Similar to J1622, an inflation of the brown dwarf by more than about 10 % can be excluded. V2008-1753 has the shortest period of all known HW Vir systems and the second shortest period of any sdB binary discovered to date. Due to the small separation distance and high temperature of the sdB, the amplitude of the reflection effect is relatively large (more than 10 %). Consequently, this system might provide the chance to detect and evaluate spectral features of the irradiated companion, similar to AA Doradus and HW Vir (Vuˇcković et al. 2008, 2014). If the companion’s spectral features are detected, the radial velocities of both components could be determined. We then could derive an unbiased mass ratio of the system


112

0.13 0.12

Rcompanion [R⊙]

0.11

0.35 M⊙

0.47 M⊙ 0.53 M⊙

q=0.10

0.1 0.09 0.08 0.07 0.06

q=0.19 0.04

0.06

0.08 0.1 Mcompanion [M⊙]

0.12

0.14

Figure 7.28.: Comparison of theoretical mass-radius relations of brown dwarfs by Baraffe et al. (2003) for an age of 1 Gyr (filled triangles), 5 Gyrs (triangles) and 10 Gyrs (diamond) to results from the lightcure analysis. Each error cross represents a solution from the light curve analysis for a different mass ratio (q = 0.10 − 0.19). The dashed vertical lines mark different values of the corresponding sdB masses. The solid line marks the most probable solution with q = 0.146, which results in an sdB mass of 0.47 M .

and obtain a unique spectroscopic and photometric solution. Higher quality and resolution spectra should also allow the detection of the Rossiter-McLaughlin (RM) effect (cf. Vuˇcković et al. 2007). This effect is due to the selective blocking of the light of the rotating star during an eclipse. The amplitude is mainly depending on radius ratio, the rotational velocity of the primary star, and the inclination of the system. As our system has a high inclination and a high radius ratio, the expected amplitude is quite high. From the RM effect it is, hence, possible to determine the rotational velocity independent from spectral line modelling. With the help of the rotational velocity we can verify, whether the sdB is synchronized, which should be the case due to synchronization theories, but is currently under debate (Schaffenroth et al. 2014c). The presence of stellar pulsations in the sdB offers further possibilities to characterize this system. Once the pulsation frequencies are fully resolved and their modes identified with higher– precision data over a longer time base, the mass and other properties of the sdB can be constrained by asteroseismology. These results can be compared to the light curve models. To date, only NY Vir (Van Grootel et al. 2013) has offered this opportunity. However, no signature of the companion could be identified in the spectrum of this system, and the masses from the light curve analysis remain biased. The combined presence of pulsations and eclipses, furthermore, offers the possibility of eclipse mapping, as done for example for NY Vir (Reed et al. 2005; Reed & Whole Earth Telescope Xcov 21 and 23 Collaborations 2006). Thereby, the eclipses can be used to determine pulsation modes, which are often difficult to uniquely identify. During the eclipse parts of the star are covered. Changing the amount and portion of regions of the star visible affects the pulsation amplitudes. The effect is changing for different pulsation modes, which can be identified in this way.

113


V2008-1753 has the potential to eventually replace NY Vir as the benchmark system for understanding sdB stars and their binary nature, if emission lines of the companion are detected. It would permit the direct comparison of independent techniques (namely light curve modelling, asteroseismology, spectroscopy, and radial velocity variations) used to derive the stellar parameters. Hence, the reliability of these methods and models could be checked as well as possible systematic errors of the derived parameters could be further investigated. Most notably, the mass determined by asteroseismology could be checked at a high precision level, if the semi-amplitudes of the radial velocity curves could be determined for both components.


Table 7.13.: Adopted light curve solution. Fixed parameters: q (= M2 /M1 ) Teff (1) g1b g2b x1 (g 0 )c x1 (i0 )c δ2d

[K]

0.146 33000 1.0 0.32 0.21 0.14 0.0


86.83 ± 0.45 2960 ± 550 1.0 ± 0.002 1.2 ± 0.05 4.10 ± 0.05 2.389 ± 0.008 0.99995 ± 0.00007 0.99926 ± 0.00068 0.026 ± 0.01 0.44 ± 0.06 0.62 ± 0.07 0.007 ± 0.001 0.0 ± 0.0


[a] [a] [a] [a]

0.246 ± 0.001 0.249 ± 0.002 0.249 ± 0.002 0.249 ± 0.002


[a] [a] [a] [a]

0.150 ± 0.001 0.154 ± 0.002 0.152 ± 0.001 0.158 ± 0.001

i Teff (2) Aa1 Aa2 Ωf1 Ωf2 L1 0 g L1 +L2 (g ) L1 0 g L1 +L2 (i ) δ1 x2 (g 0 ) x2 (i0 ) l3 (g 0 )f l3 (i0 )f Roche radiih :

a

Bolometric albedo Gravitational darkening exponent c Linear limb darkening coefficient; taken from Claret & Bloemen (2011) d Radiation pressure parameter, see Drechsel et al. (1995) e Fraction of third light at maximum f Roche potentials g Relative luminosity; L is not independently adjusted, but recomputed from r and 2 2 Teff (2) h Fractional Roche radii in units of separation of mass centres b

114

115

7.7. OGLE-GD-ECL-08577 – THE LONGEST PERIOD HW VIRGINIS SYSTEM

Figure 7.29.: Location of the twenty-one OGLE-III disk fields in the Galactic coordinates. Each field covers 35’x35’ in the sky. Two fields, CAR109 and CAR115, overlap with each other in ≈ 67%. The total monitored area is 7.12 deg2

7.7. OGLE-GD-ECL-08577 – The longest period HW Virginis system Almost all of the HW Virginis systems but for the systems we found in the course of the MUCHFUSS project, have been found due to the characteristic shape of the lightcurve. Therefore, photometric surveys are suited perfectly to look for such systems. One such survey is the OGLE (Optical Gravitational Lensing Experiment) survey. The OGLE project is a collaboration between the Warsaw University Observatory, Carnegie Observatory, and Princeton University Observatory. Observations were done in the beginning with the 1 meter Swope telescope and were then continued with the 1.3-m Warsaw telescope at the Las Campanas Observatory, operated by the Carnegie Institution of Washington. In the following we will discuss the analysis of OGLE-GD-ECL-08577. which is with a period of about 0.5 d the HW Vir system with the longest period ever discovered. OGLE is a long-term project with the main aim to detect microlensing events toward the Galactic bulge (Udalski et al. 1993; Udalski 2003). However, regular observations of the Milky Way and Magellanic Cloud stars, conducted in some fields for over 21 years, allowed the discovery and exploration the variety of variable objects. As a matter of fact in the OGLE-III Galactic Disk Fields (Fig. 7.29) 10 new HW Vir candidates were found with periods from 0.077 to 0.50 d (Fig. 7.30, Pietrukowicz et al. 2013). 7.7.1. Observations Photometry

All the data in the observation of the OGLE-III Galactic Disk Fields were collected with the 1.3-m Warsaw telescope at Las Campanas Observatory, Chile. During the OGLE-III project, conducted in years 2001-2009, the telescope was equipped with an eight-chip CCD mosaic camera with 8192 x 8192 pixels and with a scale of 0.26 arcsec/pixel and a field of view of 35’ x 35’. Each chip of the mosaic is a SITe ST-002a CCD detector with 2048 x 4096 pixels of 15 µm size. They are cooled and held at the temperature of 95 (Udalski 2003). Twenty-one fields covering the total area of 7.12 deg2 around the Galactic plane between longitudes +288◦ and +308◦ were observed. Their location in the sky is shown in Fig. 7.29. The time coverage as well as the number of data points obtained by the OGLE project varies considerably from field to field. The vast majority of the observations, typically of 1500 to 2700 points per field, were collected through the I-band filter with exposure times of 120 s and 180 s. Additional


116

Figure 7.30.: Light curves of ten newly discovered sdB type binaries arranged with the increasing orbital period.

117


observations, consisting of only 3-8 measurements, were carried out in the V-band filter with an exposure time of 240 s. The time-series photometry was obtained with the standard OGLE data reduction pipeline. The CCD reduction is based on the standard IRAF7 routines from CCDPROC. Afterwards it is processed by the main OGLE-III photometric data pipeline. The photometry software applies the image subtraction method. In the first step of reductions the shift between the frame and the reference image, which is a co-added image of several best individual images, is calculated. In the next step the difference image of the current frame is searched for objects that brightened or faded. The positions of these detections are crosscorrelated with the positions of stars detected in the reference image and two files containing the known variable stars and ’new” variable stars in the current difference image are created. Finally, the photometry of all objects identified earlier in the reference image at the position of their centroids is derived (Udalski 2003). About 345 500 detections with a signal to noise S/N > 10 were visually checked for any kind of variability. The search resulted in about 13 000 eclipsing binary candidates, ≈ 1000 ellipsoidallike candidates, ≈ 1000 pulsating star candidates, and ≈ 15000 miscellaneous variables (mostly stars with spots) (Pietrukowicz et al. 2013). The periods were then determined by the TATRY code (Schwarzenberg-Czerny 1996) and false detections were removed from the list of eclipsing binary candidates. The final OGLE-III catalog8 of eclipsing binaries in the Galactic disk, contains tables with basic parameters and time-series I- and V -band photometry (Pietrukowicz et al. 2013), We downloaded the photometry from ftp server, converted the magnitudes to relative flux, and phased the lightcurve with the given ephemeris for OGLE-GD-ECL-08577. HJD = 242735.23316 + 0.50660638(4231) · E

(7.4)

Spectroscopy

The HW Virginis system with the largest period known so far is AA Dor with a period of 0.2614 d. As the period of OGLE-GD-ECL-08577 with 0.5066 d is almost doubling the period of AA Dor, and it is relatively bright (I = 16 mag) we obtained time-series spectroscopy for this HW Vir candidate. Several spectra were taken with the ESO-NTT/EFOSC2 spectrograph from the 1-4 Feb 2014. We obtained 10 spectra with the Grism 19 covering a wavelength range from 4450 − 5110 ˚ Aat a resolution R ≈ 2200, which are suitable for the measurement of RVs only. Moreover we took two spectra with Grism 7 with a wavelength range of 3500 − 5200 AA and a resolution of ≈ 6 ˚ A, from which it is possible to derive also atmospheric parameters. All spectra were corrected with an average bias frame constructed from several individual bias frames as well as an average flat field constructed from several flat field lamps. Reduction was done with the MIDAS9 package. For the wavelength calibration several HeAr lamps were taken during the night and the lamp frame closest to the observation was used. 7.7.2. Analysis Spectroscopic analysis

The radial velocities (RVs) were measured by fitting a set of mathematical functions matching the individual line shapes to the hydrogen Balmer lines as well as helium lines using SPAS (Hirsch 2009) to the 12 EFOSC2 spectra. Polynomials were used to match the continua and a combination of Lorentzian and Gaussian functions to match cores and wings of Radial velocity curve

7

IRAF is distributed by National Optical Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with National Science Foundation. 8 ftp://ftp.astrouw.edu.pl/ogle/ogle3/OIII-CVS/gd/ecl/ 9 The ESO-MIDAS system provides general tools for data reduction with emphasis on astronomical applications including imaging and special reduction packages for ESO instrumentation at La Silla and the VLT at Paranal


118

60

radial velocity in km s-1

40 20 0 -20 -40 -60

residuals

-80 40 20 0 -20 -40 0

0.25

0.5 orbital phase

0.75

1

Figure 7.31.: RV curve of OGLE-GD-ECL-08577

the lines. The single measurements can be found in Table 7.14. As the secondary minimum of the lightcurve is exactly at phase 0.5 we can exclude eccentricity. Therefore, the RV measurements were fitted with a sine curve (vrad (φ) = K sin(2πφ/P ) + γ) with the period determined by the lightcurve. K = 47 ± 7.5 km s−1 γ = −16 ± 5km s−1 The RV curve with a fit with these parameters is shown in Fig. 7.31. The two ESO-NTT/EFOSC2 spectra with larger wavelength coverage were used to determine the atmospheric parameters of the hot subdwarf primary. We shifted them with their radial velocity and coadded both. For the determination of the parameters the hydrogen and helium lines were fitted with synthetic model spectra calculated with metal line-blanketed LTE model atmospheres (Heber et al. 2000). Atmospheric parameters

Teff = 28400 ± 1000 K log g = 5.43 ± 0.15 log y = −2.00 As the S/N of the combined spectrum is low in the higher Balmer lines (S/N= 15), we obtained large statistical errors. Hence, we do not have to consider the apparent change of parameters seen in some HW Vir systems (Schaffenroth et al. 2013) caused by the changing continuum due to the reflection effect. Figure 7.32 shows the fit of the hydrogen and helium lines with the derived parameters.

119


He I 4922 He I 4472 He I 4026


−30

−20

−10

0 ∆λ[Å]

10

20

30

Figure 7.32.: Fit of the Balmer and helium lines in the co-added EFOSC spectrum. The solid line shows the measurement, and the dashed line shows the best fitting synthetic spectrum.

Lightcurve analysis

The lightcurve of OGLE-GD-ECL-08577 shows the typical shape for an HW Vir system (Fig. 7.33). We performed a lightcurve analysis using MORO the same way as already shown in Schaffenroth et al. (2013) and Sect. 7.4, 7.5 and 7.6. We calculated only two solutions for two different q. One solution with the q corresponding to a mass for the sdB near the canonical mass and one solution corresponding to the highest possible mass for the companion. Companions with masses larger than & 0.45M are expected to be visible in the spectrum and can, hence, be excluded. Unfortunately, we can find a lightcurve fit of similar quality for both mass ratios, as often the case in a lightcurve analysis. However, deviating from the lightcurve analyses of all other HW Virginis system, it was not possible to fit the amplitude of the reflection effect with the normally used parameter range. The amplitude of the reflection effect depends on the teimperature differenece and the separation of both components. A fit of the amplitude was only possible with a very high albedo of between 6-7. This is highly non-physical. This problem has to be investigated further. Table 7.16 shows the parameter of the lightcurve solution with q = 0.267 and q = 0.14. Together with the results from the spectroscopic analysis we can determine the parameters of the system. They are listed in Table 7.15. As a additional check, we can compare the radius of the sdB


120

Table 7.14.: RVs of OGLE-GD-ECL-08577: The observations were taken with the EFOSC instrument mid−BJD −2 450 000 56690.1794435 56690.3571400 56691.3039611 56692.1841074 56692.2873668 56691.3169969 56693.0779898 56693.1377761 56693.1988405 56693.2621304 56693.3261146 56693.3494806

RV [km s−1 ] 29 ± 9 −58 ± 12 −23 ± 12 42 ± 18 17 ± 12 −6 ± 17 −13 ± 12 −1 ± 9 39 ± 14 7 ± 14 18 ± 16 5 ± 17

Table 7.15.: Parameters of OGLE-GD-ECL-08577 OGLE-GD-ECL-08577 coordinates 11:56:30.82 -62:14:35.3 (J2000.0) cv [mag] 16.0 K P q (= M2 /M1 ) i MsdB Mcomp a RsdB Rcomp log g(sdB, phot) log g(sdB, spec) Teff,sdB

[km s−1 ] [h] ◦

[M ] [M ] [R ] [R ] [R ]

[K]

47.14 ± 7.5 0.50660638 0.267 0.14 89.54 89.52 0.46 ± 0.11 2.60 ± 0.62 0.12 ± 0.03 0.36 ± 0.09 2.24 ± 0.36 3.84 ± 0.61 0.22 ± 0.03 0.37 ± 0.06 0.16 ± 0.02 0.27 ± 0.04 5.43 ± 0.07 5.71 ± 0.07 5.43 ± 0.15 28400 ± 1000

from the spectroscopic analysis with the one from the lightcurve analysis. From the photometric radius together with the mass a photometric log g can be calculated. For this solution also the radius of the companion is consistent with theoretical predictions (see 7.19). This shows that only the solution with a mass near the canonical mass gives a consistent solution. A solution with a high mass for the sdB and the companion, which is also excluded from theory, can, hence, also be excluded by our analysis. To sum up we cannot determine a unique solution for OGLE-GD-ECL-08577. However, only a solution with a mass near the canonical mass for the sdB gives a consistent solution. This means the companion is a late M dwarf with a quite low mass around 0.12 M . This was unexpected as the period is much larger, we expected a larger companion mass. However, this was also not observed for the HW Vir system with the second largest period AA Dor. Moreover, the reflection effect is much stronger, as expected for this long period. Until now we have no explanation for this. This is the only HW Vir system, for which no lightcurve solution with reasonable parameters, especially albedo, is possible. We will obtain another lightcurve of this system in the V and R band, which will hopefully help to solve this system. Moreover, there are

121


1 0.9

normalized light

0.8 0.7 0.6 0.5 0.4

residuals

0.3

0

-0.2

0

0.2 orbital phase

0.4

0.6

Figure 7.33.: Lightcurve of OGLE-GD-ECL-08577 in the I band.

two other fainter long period OGLE HW Virginis candidates, where we will obtain photometric and spectroscopic follow-up, which will hopefully also help to shed light on the reflection effect in longer period sdB+dM binaries.


Table 7.16.: Light curve solutions for different q. Fixed parameters: q (= M2 /M1 ) Teff (1) g1b g2b x1 (g 0 )c x1 (i0 )c δ2d

0.267 [K]

0.14 33000 1.0 0.32 0.21 0.14 0.0


89.54 0.247 1.00 7.21 9.64 5.16 0.9996639 0.09059 0.954 0

89.52 0.278 1.00 6.88 10.42 3.42 0.9992417 0.00039 1.00 0


[a] [a] [a] [a]

0.09698 0.09708 0.09704 0.09707

0.09720 0.09727 0.09725 0.09727


[a] [a] [a] [a]

0.07038 0.06882 0.07045 0.07058

0.07034 0.07070 0.07044 0.07069

i Teff (2) Aa1 Aa2 Ωf1 Ωf2 L1 0 g L1 +L2 (g ) δ1 x2 l3 (g 0 )f Roche radiih :

a

Bolometric albedo Gravitational darkening exponent c Linear limb darkening coefficient; taken from Claret & Bloemen (2011) d Radiation pressure parameter, see Drechsel et al. (1995) e Fraction of third light at maximum f Roche potentials g Relative luminosity; L is not independently adjusted, but recomputed from r and 2 2 Teff (2) h Fractional Roche radii in units of separation of mass centres b

122

123

7.8. PHOTOMETRIC FOLLOW-UP OF THE MUCHFUSS PROJECT

7.8. The fraction of substellar and low-mass stellar companions in hot subdwarf binaries: Photometric follow-up of the MUCHFUSS project After the analysis of single HW Virginis systems, we come now to the statistical results of the photometric follow-up of the MUCHFUSS projects. The selection of the targets due to radial velocity shifts in the continuous spectra in SDSS and not by the lightcurve, as usual the case, allowed us to determine the percentage of reflection effect binaries and substellar companions to sdB binaries. Therefore, we calculated expected amplitude of the light variations and the RV curve. As stated before, if we have a typical system with an M dwarf or brown dwarf as companion, light variations are visible, even for low inclinations. Figure 7.4 shows the expected semi-amplitude of the light variations in RB and the expected semi-amplitude of the radial velocity at different inclinations. We determined the relative semi-amplitude by calculating synthetic lightcurves for the parameters of the prototype HW Virginis and the sdB+BD system J1622 for different inclinations with MORO. Using the mass ratio and the separation of these systems we could, moreover, calculate the expected semi-amplitude of the radial velocity for different inclinations (see Fig. 7.4). We also fitted a parabola through the determined points in order to be able to get the relative semi-amplitude of the lightcurve variation A and the semi-amplitude of the radial velocity K at any inclination. for HW Vir: K = −0.00691662 i2 + 1.66477 i − 0.80223

(7.5a)

A = −6.79716 · 10−6 i2 + 0.00151838 i − 0.000361173

(7.5b)

for J1622: K = −0.00416351 i2 ∗ 0.970709 i − 0.73049

(7.6a)

A = −5.25819 · 10−6 i2 + 0.00102431 i − 0.00137412 (7.6b) where i the inclination in degree is. It is clearly visible that K and A is higher in the case of HW Vir despite its longer period due to the greater mass and radius of its companion. Because of changing conditions the quality of the observed lightcurves is not always the same. To estimate the possible amplitude of a hidden sinusoidal signal in the non-detection lightcurves we normalised the lightcurve to one and calculated the standard deviation in the RB . One difficulty in this context was that for some of the lightcurves a linear trend was found with changing airmass. This is due to the fact that the target is much bluer than the comparison stars and the atmospheric extinction is wavelength depended. This effect leads to an overestimation of the standard deviation and, hence, the measurement is even more conservative. As the maximum possible inclination, we defined the inclination at which A is equal to the measured standard deviation for the two example cases of HW Vir and J1622 (Eq. (7.5a) and (7.6a)). For the derived inclination we get the expected K from Eq. (7.5b) and (7.5b). If the radial velocity shift measured from the SDSS spectra is larger than the expected one, we can exclude systems with parameters similar to HW Vir or J1622. The period distribution of the known sdB+dM or BD systems (see Jeffery & Ramsay 2014) shows that most sdB+dM systems have periods similar to the prototype for an eclipsing sdB+dM system HW Vir. This is, therefore, a system typical for an sdB with low-mass main-sequence companion. Until now no He-sdO+dM systems have been found. Therefore, we cannot draw conclusions about the possible companion of the observed HesdOs. However, one of the He-sdOs shows light variations, which are probably due to ellipsoidal deformation of the sdB (Fig. 7.34). This points toward a compact, massive companion, as for example a massive WD companion. Not for all observed systems radial velocity shifts have been


124

measured, as not all observed systems are from the MUCHFUSS project, but some are also back-up targets, for which we choose known bright hot subdwarf stars. We cannot draw any conclusions on these stars, but we also show them for completion. The results for all observed lightcurves, except for the ones found in Fig 7.35(a),(b),(c),(d), are displayed in Tables 7.17, 7.18 and 7.19.

125


Table 7.17.: Back-up targets target primary survey σa J074508+381106 J071011+403621 J073646+220115 J234528+393505 J074811+435239 HE2208 PG0026 J030749+411401 J015026-094227 a b

sdB sdB sdB He sdO sdB sdB sdB sdB sdB

Galex Galex SDSS SDSS SDSS SPY SPY SDSS SDSS

0.008300 0.017000 0.027600 0.007150 0.005160 0.005640 0.005000 0.016680 0.006957

∆Tlcb h 0.43 1.42 1.72 1.67 1.90 1.26 2.61 1.74 2.21

standard deviation of the normalised lightcurve in RB length of the observed lightcurve

Table 7.18.: He sdO/sdOB and sdO from the MUCHFUSS project target primary σa ∆Tlcb h J141549+111213 He-sdO 0.055700 1.05 J030607+382335 sdO 0.006400 1.74 J232757+483755 He-sdO 0.007650 1.53 J221920+394603 sdO 0.006280 0.92 J090957+622927 sdO 0.024000 2.03 103549+092551 He-sdO 0.007710 2.38 J161015+045051 He-sdO 0.012000 1.70 J112414+402637 He-sdO 0.013500 2.78 J163416+22114 He-sdOB 0.004340 2.14 J012739+404357 sdO 0.010000 0.00 b

standard deviation of the normalised lightcurve in RB length of the observed lightcurve

1.04 1.03 1.02 normalized flux

a

1.01 1 0.99 0.98 0.97 1

1.02

1.04

1.06 time [d]

1.08

1.1

1.12

Figure 7.34.: Lightcurve of the He-sdO J1124 showing sinusoidal light variations

1.1

1.05

1.05

1

1

0.95 relative flux

normalised flux


0.95 0.9

0.9 0.85

0.85

0.8

0.8

0.75

0.75 0.4

0.6

0.8

1 phase

1.2

1.4

0.7 0.34

1.6

126

0.36

0.38

0.4

0.42

0.44

0.46

0.48

time in JD-2455618

(a) sdB+BD system J1622

(b) sdB+BD system J0820 in UB

1

1.12 1.10

0.95

i

Normalised flux

normalised flux

1.08

0.9

0.85

1.06

r

1.04 1.02

0.8

b

1.00

0.75 1.32 1.34 1.36 1.38

0.98

1.4

1.42 1.44 1.46 1.48

1.5

1.52

u

0.00

0.25

0.50

0.75

1.00

time in d

1.25 1.50 Time [h]

1.75

2.00

2.25

2.50

(d) pulsating sdB+dM system J0120

(c) sdB+dM system J1920

J1415

1.01 1.2

1.008 1.15

1.006

1.05

1.002

relative flux

normalised flux

1.1

1.004

1 0.998

1

0.95

0.996

0.9

0.994 0.85

0.992 1.6

1.8

2

2.2

2.4 2.6 t in h

2.8

3

(e) sdB+WD system J0507 in BB

3.2

3.4

0.8 0

0.2

0.4

0.6

0.8

1

1.2

Time[h]

(f) He-sdO J1415 in VB

Figure 7.35.: example lightcurves of systems with light variations found in the course of the MUCHFUSS project. a,b,c are three newly found HW Virginis systems (Schaffenroth et al. 2014c; Geier et al. 2011c; Schaffenroth et al. 2014b), d is a sdB+dM system with a pulsating sdB and the system is also showing the reflection effect (Østensen et al. 2013), e is probably a sdB+WD system showing ellipsoidal deformation, f is a He-sdO showing random light variations

127

Table 7.19.: Results of the analysis of the observed lightcurves in the MUCHFUSS follow-up target

a b c d e f g

sdOB sdB sdB sdB sdB+WD sdB sdOB sdB sdB sdB sdOB sdB sdOB sdB sdB sdB sdB sdB sdOB sdB sdB sdB sdOB sdOB sdB sdOB sdB sdB sdB sdB/DA sdB sdB sdOB

σa 0.027500 0.006300 0.008000 0.004000 0.003100 0.008000 0.005300 0.003520 0.003670 0.002870 0.016000 0.005570 0.010600 0.005730 0.007510 0.005786 0.010600 0.006300 0.009200 0.008145 0.008070 0.002600 0.013870 0.007300 0.005470 0.004390 0.007450 0.009500 0.008500 0.013600 0.013600 0.005190 0.004750

b ∆Tlc h

icJ1622,max

d 2KJ1622,max kms−1

icHWVir,max

d 2KHWVir,max kms−1

1.41 2.23 1.40 1.90 1.61 2.19 3.07 2.04 1.54 1.50 2.18 3.47 2.33 1.93 1.50 2.12 2.00 2.14 1.82 1.69 1.87 1.52 1.17 2.12 0.67 1.98 2.55 1.97 2.02 2.84 2.34 2.17 2.12

34.19 7.80 9.63 5.40 4.47 9.63 6.75 4.90 5.05 4.24 18.77 7.03 12.49 7.20 9.10 7.26 12.49 7.80 10.94 9.78 9.70 3.96 16.23 8.87 6.93 5.80 9.03 11.27 10.17 15.92 15.92 6.63 6.17

55.18 13.18 16.46 8.77 7.05 16.46 11.26 7.85 8.14 6.61 32.05 11.78 21.49 12.09 15.51 12.19 21.49 13.18 18.78 16.74 16.59 6.10 27.86 15.11 11.59 9.52 15.40 19.36 17.42 27.33 27.33 11.05 10.21

19.99 4.32 5.50 2.76 2.15 5.50 3.64 2.44 2.54 2.00 11.19 3.83 7.31 3.93 5.16 3.97 7.31 4.32 6.33 5.59 5.54 1.82 9.64 5.01 3.76 3.02 5.12 6.54 5.84 9.45 9.45 3.57 3.27

59.43 12.53 16.27 7.48 5.50 16.27 10.33 6.42 6.75 5.00 33.92 10.93 22.00 11.28 15.19 12.49 22.00 12.53 18.91 16.59 16.43 4.40 29.21 14.73 10.71 8.33 15.06 19.58 17.37 28.62 28.62 10.09 9.13

standard deviation of the normalised lightcurve in RB length of the observed lightcurve maximum inclination expected semi-amplitude of the RV curve maximal measured radial velocity shift time-span between the two radial velocity measurements type of system that can be excluded

◦

◦

e ∆vrad,max kms−1

67.0 24.0 105.0 168.0 ?? 53.0 65.0 91.0 154.0 83.0 79.0 191.0 88.0 70.0 123.0 42.0 237.0 164.0 42.0 31.0 40.0 110.0 83.0 49.0 259.0 140.0 64.0 48.0 ? 95.0 40.0 102.0 49.0

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

15.5 13.5 18.0 4.0 ?? 14.5 12.0 9.0 8.0 18.5 9.5 7.0 13.5 11.5 12.0 12.5 12.0 9.0 15.0 12.0 12.5 9.0 18.5 27.5 16.0 8.0 17.0 14.0 ? 30.0 18.5 27.0 27.5

f ∆Tvrad,max d

system excludedg

3195.9096 0.0154 0.0808 1.0413 ?? 2.0639 9.9390 2986.7695 1183.7390 0.0469 1151.6544 0.9988 0.0131 1080.8857 1.0019 2172.7020 68.8608 4405.6747 0.0264 0.0248 0.0126 1699.1435 0.0184 0.0163 286.2265 265.2187 0.0363 0.0301 ? 0.0158 0.0233 2250.6902 0.0163

J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 &HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir J1622 & HW Vir


J171629+575121 J215053+131650 J185129+182358 J002323-002953 J050735+034815 J073701+225637 J074551+170600 J093059+025032 J095238+625818 J112242+613758 J115358+353929 J134632+281722 J065044+383133 J224518+220746 J072245+305233 J220810+115913 J191908+371423 J083006+475150 J052544+630726 J233406+462249 J092520+470330 J032138+053840 J153411+543345 J130439+312904 J204613-045418 J011857-002546 J074534+372718 J133639+111948 J121150+143716 J113304+290221 J075937+541022 J115716+612410 J130439+312906

primary


128

250

M2,min[Mjup]

200

150

100

hydrogen burning limit

50

0 1

1.5

2

2.5

3 P [h]

3.5

4

4.5

5

Figure 7.36.: Detectable minimum mass for the companion depending on the period of the system assuming an detectable minimum RV shift of 15-20 kms−1 in 30 min. As exact massed can only be determined in eclipsing binaries, we assume that only about 37% of the systems allow a definite determination of the nature of the companion. For the rest only minimum masses can be derived.

7.8.1. Selection effects The substellar companions found until now are around 62 − 69Mjup , very close to the hydrogen burning limit. To investigate the question which companions we can detect, we have to examine the selection effects of our follow-up. We assume an sdB mass of 0.47 M . For our follow-up we selected targets with significant RV variations until 17.5 mag to get sufficient S/N for the lightcurve within a sufficiently short exposure time, as we were looking for light variations with very short periods, our maximum exposure time was set to 3 min and each star was observed for about 1.5-2.5 h. The typical errors in RV are about 15 to 20 kms−1 , which we therefore assume as the minimum detectable RV shift. As the observing conditions vary much the photometric quality varied as well, with a typical scatter of between 0.5 to 1%. As shown in Schaffenroth et al. (2014a), it is not possible to derive the inclination in a non-eclipsing system. That is why only eclipsing systems allow a mass determination. For typical periods and radius ratios in a HW Virginis system, the minimum inclination to detect eclipses is around 66 − 68◦ . The probability, that a binary has an inclination higher than a certain angle, can be calculated as described in Gray (2005), Pi>i0 = 1 − (1 − cos i0 ), for an inclination of > 68◦ the probability is 37%. The expected light variation of an reflection effect for an inclination i > 68◦ and a period of 6 h is about 5 − 10%. As the radius for companion masses between 0.02 and 0.15 M is varying only slightly with a minimum radius around 0.065 M , the same applies also for very low-mass companions. Therefore, the photometric follow-up should not miss any systems with an inclination i > 68◦ with periods smaller than 6 h, despite the fact that the stars were observed only for 1.5-2.5 h. As the time difference between the single SDSS spectra is typically 15 min, and we have at least three subsequent taken observations, we assume that the minimum RV shift we can detect is ∼ 15 − 20 kms−1 in 30 min, which is the usual error in RV. For stars with a second epoch the minimum RV shift would be even lower. Figure 7.36 shows the minimum mass that is detectable under these assumptions (i = 68◦ − 90◦ , K1,min = 15 − 20 kms−1 · P · h). With our photometric follow-up, we are able to determine

129


the masses of about 37% of the systems with companions larger than the minimum mass. However, the reflection effect would be detectable for even lower inclinations. Until now all detected HW Vir systems with confirmed BD companions have periods shorter than 2.3 h. As most HW Vir systems are found in photometric surveys this is most likely not due to an selection effect. The HW Vir system with the smallest period is V2008 with a period of 1.56 h (Schaffenroth et al., in press, Sect. 7.6). With our selection criteria, it should be possible to detect substellar companions up to a period of about 2.5-3 h (see Fig. 7.36). With a period of 1.5 h also companions of 25 to 35 Mjup could be found. In our photometric follow-up, we found three eclipsing system. The analyses of these systems are are presented in the previous sections. Moreover, only one other system showing a reflection effect together with pulsations was found (Østensen et al. 2013). The minimum mass for the companion is 0.082 M , assuming an maximum inclination i < 65◦ because of the absence of eclipses. No other reflection effect binaries could be found. Therefore, we can exclude a reflection effect with an amplitude larger than about 2%. 7.8.2. Discussion The usual way to find eclipsing sdB+dM systems was via photometric surveys like for example the OGLE survey (see Pietrukowicz et al. 2013), in which 10 new HW Virginis systems were found, with the help of the characteristic lightcurve. These systems have short periods, deep eclipses, and show a reflection effect. Such a lightcurve with these short periodicities is unique to these type of systems. Our strategy is completely different. We selected our targets from radial velocity variations. Therefore, we can really determine the percentage of systems with reflection effect and/or eclipses. Nine of our observed systems were sdOs or He-sdOs, which are not understood very well until now. All of them show RV variations, but it was not possible to determine periodicitiesm. One of our sdO lightcurves also shows random light variations, which cannot be explained (Geier et al. 2015). Only one of the He-sdOs shows a lightcurve variation that could indicate an ellipsoidal deformation of the sdO. From 49 observed sdB, sdO, or sdOB binaries we found four showing a reflection effect. Three of them showed eclipses and two of them even brown dwarf companions the first two eclipsing sdB+BD systems found (Geier et al. 2011c; Schaffenroth et al. 2014a). Therefore, we conclude that more than 8% of the sdB binaries are showing a reflection effect and more than 4% of the companions to sdBs are substellar objects, which is much more frequent as found in other binaries, which raises the question, if substellar objects can influence stellar evolution. For most of the observed sdB or sdOB systems, it is possible to exclude typical sdB+dM systems with parameters similar to HW Vir or sdB+BD systems with parameter similar to J1622 with the help of the photometric follow-up. For some targets the lightcurves are too noisy because of bad weather, and/or the measured RV shift is too small. The presence or absence of light variations can help to select very interesting targets for a spectroscopic followup. We found several eclipsing binaries, which are very important for the better understanding of the formation of hot subdwarfs and the role of substellar companions. Furthermore, they can help to improve the understanding of the common envelope phase. Systems without reflection effect and high RV shifts are good candidates for white dwarf or even more compact companions like neutron stars or black holes, which were the main goal of the MUCHFUSS project in the beginning. Figure 7.37 shows the period distribution of the known HW Virginis systems. The fact that in photometric surveys, for which the main selection effect is due to the period and not the mass of the companion, no HW Vir systems with masses below 0.062 M have been found, suggests that they are much less abundant. One explanation for that would be their destruction during the common-envelope phase. The lack of companion masses around 0.1 M cannot be

130

0

2

number

4

6


0.05

0.1

0.15

0.2

companion mass

Figure 7.37.: Distribution of the companion masses of the known HW Vir systems.

explained. Last year the new SDSS data release 10 was published were we discovered ∼ 860 new hot subdwarf stars. Therefore, there are many more interesting targets available to extend our photometric and spectroscopic campaigns. Moreover, ten more HW Vir systems were found in the OGLE survey with periods between 0.075 an 0.5 d, which almost doubles the number of known systems. There are also more photometric surveys available that are suitable to find these particular systems. This will allow us to study close binary evolution and especially the, until now, not really understood common envelope phase. With eclipsing post commonenvelope systems it is possible to constrain the current prescription of CEE by reconstructing the evolution of post-common-envelope binaries with sdB and low-mass main-sequence companions. This was already done for PCEBs with white dwarf and main-sequence companions (Zorotovic & Schreiber 2013) and could be extended to the HW Virginis systems.

7.9. STATISTICS OF HOT SUBDWARFS WITH COOL COMPANIONS

12

12

10

10

8

8

number

number

131

6 4

6 4

2

2

0

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 period[d]

12

12

10

10

8

8

number

number

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 period[d]

6 4 2

6 4 2

0

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 period[d]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 period[d]

Figure 7.38.: Period distribution: reflection effect binaries (red), HW Vir systems (grey), sum of both (blue)

7.9. Statistics of hot subdwarfs with cool companions As now already 28 HW Virginis systems, from which 17 have been analysed, are known, we have a large enough sample to investigate the distributions of the different system parameters. This can be compared to the distributions of reflection effect binaries and post common-envelope systems containing white dwarf and late-type main-sequence companions. Figure 7.38 shows the period distribution of the known sdB+dM systems. The difference between reflection effect binaries and HW Virginis systems are only the eclipses which means the inclination. The probability of an eclipse depends on the radius ratio and the separation of the system. This means that the probability of eclipses decreases with the period. The period distribution of the HW Virginis systems clearly shows a sharp maximum at around 0.1 d and then a tail until the longest period HW Vir system OGLE-GD-ECL-08577. The reflection effect binaries have larger periods as expected. They show a maximum around 0.35 d. The decrease is probably due to an selection effect, as the reflection effect gets weaker with increasing separation. That means only systems with high inclinations and/or large companions can be detected. Moreover, reflection effect binaries are harder to identify in photometric surveys. To distinguish them from ellipsoidal deformation multi-colour photometry is necessary, which is often not available. Most of the reflection effect binaries with very large periods are pulsators and have been identified due to the reason that long lightcurves have been taken to perform asteroseismology.


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number

15

10

5

0 0

0.5

1 1.5 period(d)

2

Figure 7.39.: Comparison of the period distribution of sdB+dM (grey) vs WD+dM binaries (red line)

15

10

10

number

number

8

5

6

4 2

0

0 0

0.2

0.4

0.6 Mprimary (M⊙ )

0.8

0

0.2

0.4 0.6 Mcompanion (M⊙ )

0.8

Figure 7.40.: Comparison of the mass distribution of the primary and the secondary companion of the HW Vir systems (grey) to the eclipsing WD+dM systems (red line)

The period distribution of all sdB+dM systems (HW Vir and reflection effect binaries together), however, also shows a bi-modality of the period distribution. Around a period of 0.2 d only few sdB+dM systems were found. This cannot be explained by an selection effect. WD+dM systems on the other hand have a much higher probability to be eclipsing as sdB+dM systems because of the large radius difference, which is also very sensitive to the white dwarf mass. Therefore, they are found to be eclipsing to very large periods. That is way we compare the period distribution of the eclipsing WD+dM systems with all known sdB+dM systems. This is shown in Figure 7.39. It is visible that both period distributions look very similar. For the eclipsing systems it is furthermore possible to compare the mass distributions of both the primary and the secondary. This is displayed in Fig. 7.40. As expected by theory the mass distribution of the sdBs shows a sharp peak around 0.47 M . The WD mass distribution shows a broader peak with the maximum at a similar mass.

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7.9. STATISTICS OF HOT SUBDWARFS WITH COOL COMPANIONS

10

number

8 6

4 2

0 0

0.5 M1/M2

1

Figure 7.41.: Comparison of the mass ratio distribution of the HW Vir systems (grey) to the eclipsing WD+dM system (red line)

0.18

1.2 1.1

0.16

1 0.9

0.14

0.8 0.7

0.12

0.6 0.5

0.1

0.4 hydrogen burning limit

0.08

0.3 0.2

0.06 0.05

0.075

0.1

0.25 P[d]

0.5

0.1 0.05

0.1

0.25

0.5

0.75 1

1.5

2

P[d]

Figure 7.42.: Mass of the companion as function of the period for the HW Virginis systems (left panel) and mass ratio vs period for the HW Vir systems (green x) and WD+dM systems (red +) on the right panel.

Most of the WDs have masses between 0.3 to 0.7 M . This is quite different from the mass distribution of all white dwarfs, which shows a maximum around 0.6 M with a much smaller hump at 0.4 M (Kepler et al. 2007). The reason for the smaller mass is probably the additional mass loss during the common-envelope phase. The distribution of the companions in HW Vir systems shows a peak between 0.06 to 0.2 M . As companions with larger masses should be easier to find the absence of companions with masses larger than 0.2 M cannot be a selection effect unless the period for sdB+dM systems with larger masses is much longer. The mass distribution of M dwarf companion in eclipsing WD binaries shows a bi-modal mass distribution, which is even clearer in the mass ratio distribution (Fig. 7.41). One peak can be detected around a companion mass of 0.15 M another peak around 0.35 M . The first peak coincides with the peak found in eclipsing sdB binaries but


134

seems shifted to a bit higher masses. To correct for the broader WD mass distribution the mass ratio distribution is shown. It is clearly visible that the mass ratio distribution shows a broad peak around a mass ratio of 0.32 as expected by the mass distribution. The mass ratio of the WD+dM systems shows the same peak together with a second peak around a mass ratio of 0.65. Four companions to WDs have even larger masses as the WDs. The question is whether this indicates a population similar to sdB+dM systems as well as another population. As all sdB+dM systems will evolve to WD+dM systems but they are not the only progenitors this statement is reasonable. As already stated before the common-envelope phase is still poorly understood. In a rather simplistic picture the orbital energy of the binary, which scales with the mass of the companion, is deposited into the envelope. If a more massive companion ejects the common envelope earlier, and therefore at a wider orbit than a less massive companion, a correlation between orbital period and minimum companion mass would the expected. However, even if the core masses of the sdB progenitors were very similar, their total masses (core + envelope) might have been quite different, implying different energies to expel the envelope and different final orbital separations. This can partly explain that no correlation can be seen (see Fig. 7.42). Only the substellar companions show the periods shorter than the rest. For all M dwarf companions no correlation is apparent and even the companion to the HW Vir system with the by far largest period OGLE-GD-ECL-08577 has a companion with a quite small mass of only 0.12 M . There is also no correlation for the mass ratio with the period for sdB/WD+dM systems. It only looks like that there is a minimum mass ratio that is growing with the period, which could however be a selection effect, as low-mass companions are more difficult to detect as the period increases.

8. Spectrum Synthesis in the UV The second part of this thesis deals with the analysis of B stars in the UV and the investigation of the unique runaway star HD 271791. In the optical spectra of B stars few metals show spectral lines only some lines (e.g., C, N, O, Si, S). The situation changes in te UV spectral region, where larger number of elements, in particular of the iron group, give rise to a line forest. This comprises also elements beyond the iron group, which are most interesting in connection with the investigation of nucleosynthesis in a core-collapse supernova. In order to facilitate quantitative analyses for the various chemical species, the spectrum synthesis in the UV had to be extended to account for these, which is described in the following.

8.1. Hybrid LTE/NLTE approach The calculation of a model atmosphere and the resulting spectrum in full NLTE can be highly time consuming on the order of tens of hours on a modern CPU. Even then the complexity of model atoms has to be restricted e.g., by the use of superlevels, i.e. by binning a large number of energy levels into one. While this approach is sufficient for the computation of the model atmosphere, the calculation of realistic synthetic requires a more detailed treatment. Moreover, the determination of the stellar parameter and the abundances typically relies on a grid of synthetic spectra covering a multi-dimensional parameter space (Teff , log g, ξ, n(x), ...), which makes the calculation of a large number of synthetic spectra necessary. To limit the numerical effort and use as complex model atoms as possible we employ a hybrid LTE/NLTE approach, i.e. we calculate the atmospheric structure in LTE, and perform line formation calculations in NLTE. This approach is discussed in detail by Nieva & Przybilla (2007) and Przybilla et al. (2011), who also have shown that this is consistent with full NLTE calculations for B-type stars on the main sequence. It is based on the idea that NLTE effects affect the individual spectral lines through departure of the population numbers from LTE values via the line source function, but the overall effects on the atmospheric structure are small, at least in the line forming region. The differences between the atmospheric structure calculated in LTE (Atlas 9, Atlas 12) and NLTE (Tlusty, Fastwind) codes are shown in Fig. 8.3 and will be discussed in detail later. The calculation of a synthetic spectrum is performed in several steps, which use different codes: • Atlas 12 (Kurucz 1996): computation the atmospheric structure in LTE • Detail (Giddings 1981; Butler & Giddings 1985): based on the fixed stellar atmosphere calculated by Atlas 12, the coupled radiative transfer and statistical equilibrium equations are solved by Detail to obtain the population numbers and the radiation field in NLTE. An important simplification in the hybrid LTE/NLTE approach with respect to full NLTE calculations is that the population number densities of the individual elements are computed separately, i.e. they are treated as a trace species. The line opacity due to other metals is approximated via opacity sampling in LTE usually, as are the metal bound-free background opacities. Hydrogen and helium are always treated in NLTE. • Surface (Giddings 1981; Butler & Giddings 1985): based on the population numbers determined by Detail, the final synthetic spectrum is calculated by Surface using a

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CHAPTER 8. SPECTRUM SYNTHESIS IN THE UV

136

fine frequency grid and detailed line profiles.

8.2. Calculation of oscillator strengths For the linelists used in Surface to calculate the synthetic spectra the line wavelength and the oscillator strength, which is directly related to the line strength, are the most important parameter. Hence, I will give hear a short overview about the different methods used to the oscillator strengths used in this thesis. These oscillator strengths were adopted from different sources. Most of them are calculated, with several teams applying different ab-initio methods. Some were measured in the laboratory. In the following a short overview over the different oscillator strength determinations will be given. Critically evaluated oscillator strengths are provided by the NIST Atomic Spectra Database1 . However, for heavier elements little data is available there. Therefore, the main source of oscillator strengths were the linelists by Kurucz2 , who collected atomic data from different sources or calculated them with the atomic structure codes by Cowan 3 . Moreover, several other sources were used as indicated in Tables A2 and A3. 8.2.1. Experimental measurement of oscillator strengths Experiments in absorption and emission spectroscopy have been developed for the determination of oscillator strength values. The state-of-the-art is reviewed by Wahlgren (2010). In emission line spectroscopy an excited level is populated and the subsequent radiation emitted upon its decay is measured. In time-dependent experiments also the rate of decay of the upperlevel population and the mean lifetime τj of the excited level can be measured. A conversion between emission and absorption oscillator strength is given by the relation gj fij = − fji (8.1) gi where gj and gi are the statistical weights of the upper and lower level of the transition. Highly important in this context is the so-called branching fraction BF , which is the ratio of the intensity of the line of interest relative to the combined intensity of all emission lines originating from the same upper level. Finally, the oscillator strength can be derived by: gj (BF )ji (8.2) fji = 1.499 · 10−8 λ2 gi τj where the wavelength λ is given in ˚ A and the life time τj in 10−8 s. It is also possible to determine oscillator strength values directly from emission line intensity calibrated by already published values. For this also the temperature of the arc source and the electron density have to be known. 8.2.2. R-matrix method For the calculation of transition data and electron excitation cross-sections the R-matrix method is one of the most accurate and is used for the atomic data in the NLTE model atoms and some of the oscillator strengths. ( It solves the many-body ) time-independent Schrödinger equation : N +1 N +1 X X 2Z 2 HN +1 Ψ = EΨ = −∇2i − + Ψ (8.3) r r i ij i=1 j>i The first term of the Hamiltonian describes the kinetic energy of the electrons, the second the potential energy of the electrons in the field of the nucleus and the third the Coulomb interactions of the electrons with each other. 1

http://www.nist.gov/pml/data/asd.cfm http://kurucz.harvard.edu/linelists/ 3 https://www.tcd.ie/Physics/people/Cormac.McGuinness/Cowan/ 2

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8.2. CALCULATION OF OSCILLATOR STRENGTHS R-matrix boundary

r 2400 ˚ A), if possible because of the possibly lower reliability of our modeling in the far-UV (see Chapt. 8). We calculated only LTE models for the iron group elements other than iron. To minimize effects from neglected NLTE departures, we only considered lines of the main ionization stage, which depends on the temperature and therefore could differ from star to star. The resulting abundances for the four stars are summarized in Table 9.2 and 9.3. The uncertainties are 1-σ errors from the scatter in the abundances determined from the single lines. That implies that we did not consider the systematic errors due to uncertainties in the atmospheric parameter determination but only systematic errors caused by inaccurate atomic data. The uncertainties quoted for the abundances derived from the optical are only statistical errors caused mainly by the noise in the spectrum, also not considering the uncertainties in the atmospheric parameter determination. It is obvious that the uncertainties in the optical are much lower than the errors in the UV. 11

http://www.sai.msu.su/gcvs/gcvs/iii/vartype.txt

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9.2. ABUNDANCES

0.4 ι Her HR1861 HR1840 υ Ori

0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 C

N

O Al Si Ti

V Cr Mn Fe Co Ni Cu Zn

Figure 9.5.: Abundances for the four stars of different temperatures determined from the UV spectrum relative present-day cosmic abundances (CAS) from 63 mid B-type to late O-type stars (Irrgang 2014). The abundances from the iron group are compared to meteoric solar values. The errors are given by the standard deviation of the abundances determined from single lines.

Table 9.2.: NLTE abundances determined from the UV of four bright B stars star CASa ι Her HR 1840 HR 1861 υ Ori a

optical UV optical UV optical UV optical UV

C 8.35 8.44 ± 0.02 8.43 ± 0.05 8.30 ± 0.02 8.41 ± 0.12 8.24 ± 0.02 8.24 ± 0.09 8.25 ± 0.02 8.38 ± 0.09

N 7.77 7.83 ± 0.02 7.66 ± 0.08 7.70 ± 0.02 7.69 ± 0.12 7.73 ± 0.01 7.61 7.59 ± 0.01 7.59

O 8.70 8.81 ± 0.02 − 8.75 ± 0.03 8.71 8.65 ± 0.02 8.71 ± 0.03 8.44 ± 0.02 8.73 ± 0.08

Al 6.26 6.31 ± 0.02 6.19 ± 0.07 6.22 ± 0.02 6.29 ± 0.18 6.27 ± 0.03 6.25 6.23 ± 0.03 6.15

Si 7.46 7.56 ± 0.02 7.37 ± 0.17 7.38 ± 0.03 7.40 ± 0.14 7.31 ± 0.02 7.39 ± 0.14 7.24 ± 0.02 7.14 ± 0.14

Fe 7.37 7.36 ± 0.02 7.41 ± 0.12 7.35 ± 0.02 7.41 ± 0.11 7.37 ± 0.02 7.36 ± 0.11 7.24 ± 0.02 7.43 ± 0.15

Present-day cosmic abundances (CAS) from 63 mid B-type to late O-type stars (Irrgang in prep.).

Table 9.3.: LTE abundances determined from the UV of four bright B stars star solara ι Her HR 1840 HR 1861 υ Ori a

Ti 4.91 4.82 ± 0.08 4.81 ± 0.08 4.94 ± 0.14 5.05 ± 0.13

V 3.96 3.71 ± 0.22 3.96 ± 0.17 3.93 ± 0.04

Cr 5.64 5.49 ± 0.18 5.60 ± 0.10 5.61 ± 0.21 5.64 ± 0.09

Mn 5.48 5.25 ± 0.23 5.30 ± 0.08 5.24 ± 0.25 5.52 ± 0.13

Co 4.87 4.86 ± 0.11 4.89 ± 0.05 4.94 ± 0.05 4.88

Ni 6.20 6.12 ± 0.10 6.21 ± 0.10 6.02 ± 0.24 6.14 ± 0.13

Cu 4.25 4.21 ± 0.17 4.11 ± 0.2 4.12 ± 0.23 4.22

Zn 4.63 4.47 ± 0.12 4.45 ± 0.15 4.56 4.45 ± 0.15

meteoritic solar values from Asplund et al. (2009)

This is mainly due to the thorough testing of the atomic data employed in the model atoms in the optical, which has so far not been undertaken for the UV spectral range (i.e. leaving room for improvements). The observed spectrum of ι Her is compared to a model calculated, based on these abundances

CHAPTER 9. SPECTROSCOPIC ANALYSIS OF FOUR BRIGHT B STARS IN THE UV

154

and the atmospheric parameters from Table 9.1 in Appendix D, together with the residuals. The comparison looks overall good. Only few lines are absent in the model. The residuals reveal still deviations between model and observation in the line depths, which reflects the large scatter in the abundances in particular in the far-UV. The abundances determined from the optical spectrum were compared to the present-day cosmic abundances (CAS) from 63 mid B-type to late O-type stars (Irrgang 2014). These abundances agree very good with the CAS determined by Nieva & Przybilla (2012) with only small deviations. The comparison is shown in Fig. 9.5. The abundances for the NLTE elements match the abundances determined from the optical spectrum very well. Within the errors they are all consistent. Therefore, we are confident that the determination of abundances based on our synthetic UV models is reliable. Hence, we are convinced that also the abundances for the iron group are reliable. This is also indicated by the good agreement with the solar abundances that are very similar the the present-day cosmic abundances derived from nearby B stars.

10. The extreme runaway HD 271791 HD 271791 is a bright (V=12.258), well known, apparently normal, B-type star at high Galactic latitude (l = 276.65, b = −29.57). Because of its large distance to the Galactic plane HD 271791 was regarded a runaway B star. HD 271791 attracted attention because of its very high radial velocity of 442 km s−1 (Kilkenny & Muller 1989). Due to the discovery of the hyper velocity stars (HVS), which are unbound to the Galaxy, a further investigation of this star became interesting. As it is much brighter than the other HVS it can be studied in great detail. Heber et al. (2008) re-investigated this star by using high-resolution, high-S/N spectra to constrain the nature of the star, its mass, distance, and evolutionary lifetime. Moreover, they investigated the space motion of HD 271791 to constrain its place of origin. They stated that HD 271791 is a massive B giant (Teff = 17800±1000 K, log g = 3.04±0.1) with a mass of M = 11± M and an age of 25±5 Myr. From the proper motions of the star they get a Galactic rest-frame velocity of 530 − 920 km s−1 , which implies that this star is indeed unbound to the Galaxy. Moreover they calculated trajectories for HD 271791 back to the Galactic plane to identify its place of origin and found the birth-place to be on the outskirts of the Galactic disc with a Galactocentric distance of & 15 kpc. They excluded the Galactic center as a possible origin, as the flight-time required to reach the current position exceeds the evolutionary life-time by a factor of three. As the Hills-mechanism can be excluded to be responsible for the acceleration of HD 271791, Przybilla et al. (2008) performed a quantitative analysis of the star to distinguish between the binary-supernova scenario and the dynamical ejection scenario. An accurate determination of the surface composition confirmed the low [Fe/H] expected for a star born in the outer Galactic rim. The detected α−enhancement points towards an extreme case of the binary-supernova runaway scenario. The evolution of a binary with a very massive primary (M & 55 M ) can lead to a suitable progenitor. After a common-envelope phase a Wolf-Rayet star (WR) with a close main sequence star of spectral type B is formed. An asymmetric supernova-explosion of the WR could explain both the α−enhancement and the ejection at high velocity. As a high kick velocity is necessary to explain the very high Galactic rest-frame velocity of the star Gvaramadze (2009) doubted the responsibility of the BSS for the ejection of HD 271791. In order to shed further light on the topic we re-investigate here this highly interesting star by using higher S/N optical spectra taken with ESO-VLT/UVES, as well as UV spectra taken with HST/STIS and COS to investigate the abundances of the heavier elements. Moreover, we want to investigate the supernova scenario with simulations of the ejection of the companion in the supernova scenario calculated with the parameters of the progenitor system using the equations by Tauris & Takens (1998), analogue to Tauris (2015).

10.1. Analysis of the optical spectrum To improve the abundance analysis in the optical high S/N spectra in several set-ups together covering the entire wavelength-range from 3050 to 10000 ˚ A where taken with the ESOVLT/UVES spectrograph at Cerro Paranal at 14 and 20 April 2009 with a resolution of about R = 30000. All spectra were reduced with the ESO-pipeline for UVES based on Reflex1 (Freudling et al. 2013). It provides a graphical user interface to reduce the data fully 1

https://www.eso.org/sci/software/reflex

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CHAPTER 10. THE EXTREME RUNAWAY HD 271791

156

30000 25000

flux

20000 15000 10000 5000 0 3050 3100 3150 3200 3250 3300 3350 3400 3450 wavelength [Å] Figure 10.1.: UVES spectrum (red line) compared to the spectrum corrected by molecfit, with the best fitting ozone abundance.

automatically based on the ESO-pipelines for the VLT instruments. For the analysis all spectra were normalized and co-added. Moreover, we corrected the spectrum for telluric the features. 10.1.1. Correction of the O3 -Huggins Bands Our UVES spectrum in the optical was taken with the ESO-VLT/UVES spectrograph on the ground. The absorption spectrum of the Earth’s sky (shown in Fig. 10.2) is therefore imprinted on the absorption spectrum of the star. From λ = 7000 − 10000 ˚ A the spectrum is dominated by molecule bands of H2 O an O2 in the air. These are very sharp lines with little thermal broadening and can hence, easily be distinguished from the absorption lines of the star and be removed. However, from 3000 to 3500 ˚ A we find the O3 Huggins bands. These are broad bands caused by the blends of many lines with similar wavelengths. They have similar widths to one order in the echelle spectrum and are therefore more difficult to correct for. Hence, we use the program molecfit that was developed by the ESO-in kind group in Innsbruck for the telluric correction in this wavelength range. This program is fitting the abundances of the most relevant molecules in the atmosphere and calculates a transmission spectrum on a theoretical basis (Smette et al. 2015). The wavelength range from 3000 to 3500 ˚ A is covered by two different spectra observed within one hour. We fitted both spectra in regions without stellar lines to determine the abundances of ozone in the atmosphere. For the first spectrum we obtained a molecular gas column of 4.662 · 10−1 ± 2.056 · 10−3 in ppmv (parts per million by volume), for the second spectrum we measured 4.755 · 10−1 ± 1.700 · 10−3 ppmv. Both measurements are only sightly different.

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10.1. ANALYSIS OF THE OPTICAL SPECTRUM

H2O

Transmission

Chappuis ozone absorption bands 1 0.8 0.6 0.4 0.2 0

HO 2 O 2 (γ band)

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single H2O lines (5)

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15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30 wavelength [µm]

Figure 10.2.: Synthetic absorption spectrum as calculated by molecfit of the sky between 0.3 and 30 µm, adopted from Smette et al. (2015)

Figure 10.1 shows the original as well as the corrected spectrum. The ozone bands are corrected very well by molecfit, but the correction degrades the S/N in particular in the bluest part of the spectrum.


158

10.1.2. Fundamental parameters and abundances from the optical spectrum For the analysis of the normalized and corrected spectrum we employed the method introduced by Irrgang et al. (2014), which fits the spectrum simultaneously using the same grid of synthetic spectra. To find the best solution a χ2 minimization is performed using different minimization algorithms (e.g., simplex algorithm, gradient method). Because of the large number of indicators the statistical error is small. However, the systematic errors are from our experience about 2% in Teff and 0.1 dex in log g. Taking this errors into account we can determine systematic errors for the abundances. The position in the Teff − log g-diagram was then compared to evolutionary Table 10.1.: Parameters of HD 271791 Teff [K] 18700 ± 370 ± 40 R [R ] 15.1 ± 1.5

log g [cgs] 3.16 ± 0.1 ± 0.02 M [M ] 11.7 ± 0.5

ξ [km s−1 ] 5.9 ± 1 age [Myr] 18 ± 2

v sin(i) [km s−1 ] 128 ± 1 log L [L ] 4.44 ± 0.07

ζ [km s−1 ] 22 ± 4 d [pc] 22.0 ± 2.55

vrad [km s−1 ] 443 ± 1

tracks, as described in Sect. 6.2.2 to derive the mass, radius, age, and luminosity of the star. A fit of the measured photometry to a synthetic spectrum calculated for the atmospheric parameters, furthermore, determined the spectroscopic distance. All parameters of the star are summarized in Table 10.1. The results of our new analysis of the higher S/N spectrum are consistent with the results that were obtained by Przybilla et al. (2008). The measured abundances are summarized in Table 10.2 with statistical and systematical errors. To study Table 10.2.: Abundances of HD 271791 C 8.03 ± 0.02 ± 0.07 Al 5.99 ± 0.02 ± 0.07

N 7.39 ± 0.02 ± 0.07 Si 7.27 ± 0.035 ± 0.1

O 8.39 ± 0.015 ± 0.07 S 6.94 ± 0.02 ± 0.07

Ne 7.91 ± 0.022 ± 0.07 Fe 7.00 ± 0.03 ± 0.07

Mg 7.15 ± 0.025 ± 0.1

the supernova scenario we perform a differential abundance study by comparing the abundances of HD 271791 to those from a representative sample of 63 nearby B-stars by Irrgang et al. (in prep.), which allows us to constrain the abundances of the supernova ejecta accreted by the runaway star. This is shown in Fig. 10.3. As it is not expected that the core-collapse SN ejecta that polluted the atmosphere of the runaway contained much iron, we use iron as a baseline. The iron abundance in HD 271791 is ∼ 0.3 dex lower than in the comparison sample. This is consistent wit the star originating from the metal-poor outskirts of the Galaxy. On the other hand, several of the α−elements, e.g. Ne, Mg, Si and S, are enhanced compared to abundance values expected for the metallicity of HD 271791. To compare the abundances to calculated supernova yields some assumptions about the binary evolution and the accretion of the supernova ejecta have to be made. We employed the same assumption as used by Przybilla et al. (2008). To explain the extreme kinematic properties (see the next section for details) the progenitor system had to have been in a very tight binary system. That can only be explained, if the system has undergone a common-envelope phase. This happens only for mass ratios q = M1 /M2 ≤ 0.2. Therefore the companion of the runaway star had to have an initial mass ≥ 60M . The energy deposited in the envelope due to the spiral-in of the companion because of friction in the envelope leads to the ejection of the primary’s hydrogen envelope. Accordingly, a binary system consisting of a WR and an earlytype main-sequence B star is the most probably progenitor system of the SN-event that kicked out HD 271791. The radius of a 12 M star on the main-sequence is about 4-5 R . The radius

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10.1. ANALYSIS OF THE OPTICAL SPECTRUM

0 -0.05 -0.1

[X/H]

-0.15 -0.2 -0.25 -0.3 -0.35 -0.4 C

N

O

Ne

Mg Al Element

Si

S

Fe

Figure 10.3.: Abundances of HD 271791 as determined from the optical spectrum relative to a representative B-star sample (Irrgang et al. in prep.). The baseline metallicity of HD 271791 relative to the B-star sample, [Fe/H], is marked by the solid line.

of a WR star ≤ 20 M is about 1-2 R . Hence, the separation of the system can be as low as 10 R , so that the system is still detached, which means both stars are inside their Roche lobe. Due to the dense and strong wind of the WR star, at this point mass will probably transfered to the companion by wind accretion. We estimate that 0.04 M of material rich in C, and less abundant in O and Ne could be deposited on the surface of the runaway progenitor. At the end of its lifetime the WR star will probably experience a core-collapse supernova of type Ic or a hypernova, if the initial mass was more than 100 M , onto a black hole with a mass around 5 M . Such an scenario is discussed by Fryer et al. (2002) in more detail. As the mass of the companion is changing abruptly and the (proto-) black hole experiences a kick the binary is disrupted and the runaway is released with about its orbital velocity. Thereby the second, major accretion event onto HD 271791 happened. The interaction of the runaway with the expanding SN shell is a complex hydrodynamical process involving ablation of the outer layers of the runaway and accretion from the shell, which is not completely understood (Fryxell & Arnett 1981). Moreover, interaction with fall-back material from the explosion may be significant. Therefore, we made a conservative assumption that only 10 % of the ejecta that could be accreted (Macc = Mejecta R22 /4a2 ) is actually deposited on the surface of the runaway. Hence, about 0.04 M of heavy elements is accreted of the 10 M heavy metals expelled in total. On the other hand ∼ 1% (0.1 M ) of the secondary’s mass is ablated from the surface layers including most of the material accreted from the WR wind (Fryxell & Arnett 1981). We also have to account for mixing of the accreted material with unpolluted matter from deeper layers for the past ∼ 13 Myr since the SN. In radiative envelopes the mixing is very slow and can be approximated by diffusion (Maeder & Meynet 2000). We assume a mixing of 0.12%/0.08% of the HN/SN ejecta with 1 M unpolluted envelope material. Figure 10.4 shows a comparison of the measured the elemental abundances of the SN ejecta considering all before mentioned assumptions (normalized to iron) with hypernova/supernova yields of Nomoto et al. (2006). A qualitative agreement between theory and observation is reached for both the hypernova and the supernova yields. Only the oxygen abundance is smaller than would be expected by theory. However, that may be explained because of the use of integrated yields. Chemical homogeneity is not expected within SN ejecta. Therefore, detailed simulations of the SN explosion and of the accretion of the SN ejecta on the runaway are


160

Figure 10.4.: Abundances of HD 271791 (normalised to iron) compared to hypernova/supernova (HN/SN) yields of Nomoto et al. (2006)

required to improve on the quantitative understanding. In any case, the observed enrichment in the α-elements indicates an ejection of HD 271791 by a SN explosion in a very tight system. Hence, the BSS is the most probable explanation for the ejection of HD 271791.

10.2. Kinematics The Hipparcos satellite measured proper motions for HD 271791, which are listed in Table 10.3 together with photometric dots from Vizier2 . Together with the radial velocity determined by the Doppler shift of the spectrum and the (spectroscopic) distance it is possible to derive the rest-frame velocity of the star. Table 10.3. proper motion µα cos(δ) µδ mas yr−1 -1.08 6.75 ±1.27 ±1.45

u’

HP

3520 12.53 ±0.02

4020 12.277 ±0.01

Photometry B g’ V λ0 [˚ A] 4440 4820 5540 12.12 12.08 12.272 ±0.129 ±0.02 ±0.203

r’

i’

z’

J

H

6250 12.44 ±0.02

7630 12.68 ±0.02

9020 12.88 ±0.02

12500 12.596 ±0.024

16500 12.581 ±0.021

We traced the orbit of the star back to the Galactic plane using different models for the Galactic potential taken from Irrgang et al. (2013). We performed 100000 Monte-Carlo runs by varying the kinematically relevant parameter within the given error margins. The results of the kinematic analysis are summarised with 1-σ errors in Table 10.4 . We derived coordinates (x,y,z) in a right handed Cartesian coordinate system (with the Galactic center at (0,0,0) and the Galactic disc in the x-y plane and with x pointing from the Sun to the Galactic center) the coordinates, the current velocity vx , vy , vy , the Galactic rest-frame velocity vgrf , the escape velocity vesc with the probability of a bound orbit Pb , and the ejection velocity vej , which 2

http://vizier.u-strasbg.fr/vizier/sed/

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10.2. KINEMATICS

28

-28 0

0 -28

28

⊙+

z (kpc)

6

0

-6

⊙+

x (kpc)

⊙ +

y (kpc)

Figure 10.5.: Three-dimensional orbits of HD 271791. The nine trajectories (red lines; arrows indicate the star’s current position) are traced back to the Galactic plane and sample the mean kinematic input data as well as variations in the distance, proper motions, and radial velocity. The black rimmed, blue shaded areas mark the 1-σ and 2-σ region for the intersection with the plane. The positions of the Sun and the Galactic center are marked by a yellow and a black +, respectively. Based on Milky Way mass Model I from Irrgang et al. (2013).

assumes an ejection with the Galactic rotation (+230 km s−1 ), the flight-time τflight , and the birth-place of HD 271791 (xd ,yd ,zd ). The current position of HD 271791 is about 10 kpc below the disc in the Halo. With a restframe velocity of 735 ± 145 km s−1 it is probably unbound to the Galaxy. Only 4 − 5% of the orbits result in velocities smaller than the escape velocity, which are, hence, bound. Assuming an ejection of the runaway with the Galactic rotation we need only a ejection velocity from the binary system of 505 ± 145 km s−1 to account for the observed rest-frame velocity. The birth-place was traced back to the outskirts of the Galactic disc with a Galactocentric distance of 21 ± 7 kpc. Figure 10.5 shows three-dimensional representations of the orbit of HD 271791. The birth-place is marked as a blue-shaded area, showing the 1-σ and 2-σ region for the intersection with the plane. The Galactic center is excluded completely within 3-σ as a possible birth-place not only because the flight-time to reach from the Galactic center to the current position would be about 3 times the evolutionary age. Our findings are overall consistent with the former kinematic analysis done by Heber et al. (2008). The evolutionary age of HD 271791 determined from the Teff − log g diagram is with 18 ± 2 Myr slightly smaller than the age given by Heber et al. (2008) (25 ± 5 Myr). With a flight-time of 37 ± 18 Myr one may see a discrepancy between flight-time and age of HD 271791. For the comparison also the lifetime of the companion of about 5 Myr has to be considered. Therefore, within the 1-σ errors no overlap can be found. In Fig. 10.6 we show the possible ejection points in the x-y plane, which results in a flight-time below 20 (3.2%), 25 (17.8%), and 35 Myr (57.2 %). However, the determination of the age strongly depends on the stellar evolution models, which


162

Table 10.4.: Kinematics of HD 271791 model AS1 MN2NFW MN3TF

x -6.2 ±0.10 -6.2 ±0.10 -6.2 ±0.10

y [kpc] -19.0 ±0.8 -19.0 ±0.8 -19.0 ±0.8

z

vx

vy

-10.9 ±0.5 -10.9 ±0.5 -10.9 ±0.5

-650 ±155 -625 ±155 -635 ±155

-155 ±70 -240 ±75 -230 ±75

vz

vgrf [km s−1 ] -300 735 ±115 ±145 -340 750 ±100 ±140 -335 750 ±100 ±140

vgrf − vesc

vej

185 ±145 200 ±140 200 ±140

505 ±145 520 ±140 520 ±140

Pb [%] 5.2 3.8 4.3

xd 18.2 ±13 18.2 ±12 18.9 ±8

yd [kpc] -10.4 ±8 -10.2 ±7.5 -10.3 ±8

rd 21 ±7.0 20.9 ±6.6 21.5 ±7.8

τflight [Myr] 37.4 ± 18 36.4 ± 18 37.2 ± 19

1

revised Galactic gravitational potential by Allen & Santillan, Model I in Irrgang et al. (2013) potential with a Miyamoto & Nagai bulge and disk component and a Navarro, Frenk, & White dark matter halo, Model III in Irrgang et al. (2013) 3 potential with a Miyamoto & Nagai bulge and disk component and a truncated, flat rotation curve halo model 2

5 0

sun

GC

y [kpc]

-5 -10 -15 -20 HD271791 -25 -10 -5

0

5 x [kpc]

10

15

20

Figure 10.6.: Ejection and current position of HD 271791 in the x-y plane. The red squares mark the crossing of the Galactic disc for orbits with τ < 20 Myr (3.2% of total orbits); green squares: τ < 25 Myr (17.8% of total orbits); pink squares prob τ < 35 Myr: 57.2%

are for single-stars. It has been found that mass transfer in a binary system can rejuvenate the companion. As the evolution in a close binary deviates significantly from single-star evolution this is only an estimate. Already 57.2% of the orbits have a flight-time smaller than 35 Myr. The mismatch between the evolutionary lifetime and the measured flight-time of HD 271791 has to be investigated further. Gvaramadze (2009) doubted the binary-supernova scenario could be responsible to accelerate a B main-sequence star to velocities as observed for HD 271791. He suggested that HD 271791 was ejected by the dynamical ejection scenario while being a member of a massive post-supernova binary. They claim that the supernova could not disrupt the binary system, which means the 12 M B MS-star together with a 5 M black hole remained gravitationally bound. As most massive stars are formed in open clusters the probability of dynamical interactions in a young, dense cluster with other binaries or stars is very likely. Runaways produced by binary-binary encounters are frequently ejected at velocities compared to the orbital velocities of the binary components (Leonard 1991). Moreover, they proposed another possibility involving a close

10.2. KINEMATICS

0

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163

0

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100

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theta

Figure 10.7.: Ejection velocity of HD 271791 depending on the angle θ between kick vector and the direction of motion of the exploding star and the kick velocity [300 km s−1 (black line), 500 km s−1 (red line), 750 km s−1 (green line), 1000 km s−1 (blue line), 1200 km s−1 cyan line]; the horizontal lines give the measured rest-frame velocity-230 km s−1 and the error margins

encounter between massive hard binaries and a very massive star. However, in both scenarios normally the least massive object is ejected (Heggie 1975), which is the black hole in our case. Moreover, their simulation did not consider Galactic rotation and assumed an unrealistically high mass of 10 M for the black hole. Hence, we repeated the simulation of the ejection velocities with the parameter determined in our new analysis. The simulation calculates the ejection velocity of the secondary based on the equations (44-47) and (54-56) given in Tauris & Takens (1998). Figure 10.7 shows a recalculation of Fig. 1 from Gvaramadze (2009). This shows the ejection velocity of HD 271791 depending on the angle θ between kick vector and the direction of motion of the exploding star for different kick velocities. For θ between 100 − 250◦ the ejection velocity is not defined, which means the binary remains bound. It is obvious that for all calculated kick velocities solutions can be found that explain the minimum ejection velocity. However, to explain the maximum possible velocity a large kick of 1200 km s−1 is required. Furthermore, we also performed a Monte-Carlo simulations with 106 MC runs using an isotropic kick distribution to investigate the ejection velocities as done by Tauris (2015). This is shown in Fig. 10.8. For a kick velocity of 300 km s−1 the minimum rest-frame velocity of HD 271791 is reached by 10% of the Monte-Carlo runs. To get the maximum velocity of HD 271791 on the other hand a kick velocity of at least 1200 km s−1 is needed and only 1% of the runs reach that high velocity. But there is no evidence yet for such a large kick of an black hole (e.g., Gualandris et al. 2005). In summary we can say that an ejection velocity until the mean rest-frame velocity found in our kinematic analysis should be possible to be explained with the binary-supernova scenario. For higher velocities the scenario becomes unlikely. With the current available proper motions and the spectroscopic distance a more accurate and more precise kinematic analysis is not possible. However, the Gaia satellite is measuring parallaxes and proper motions with an accuracy < 20 µas, which will result in an error in d of 0.5 pc and


164

800

top 10% top 1%

700 600

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500 400 300 200 100 0 0

200

400

600

800 vkick

1000

1200

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1600

Figure 10.8.: Simulated ejection velocities of HD 271791 as a function of kick velocity using the equations from Tauris & Takens (1998); the dotted vertical lines give the measured rest-frame velocity−230 km s−1 and the error margins.

an proper motion error of about < 20 µas for HD 271791. The catalogue is expected in 2020, with first results becoming available already 2017. This will facilitate tighter constraints to be derived to distinguish between the possible scenarios.

10.3. Analysis in the UV Two settings with HST/STIS and HST/COS were employed to measure spectra of HD 271791, covering the 1600 − 3120 ˚ A and 1130 − 1795 ˚ A, respectively. We also acquired a low-resolution long-slit spectrum to verify the flux calibration of the STIS and COS spectra. In order to construct a SED and check the flux calibration, we downgraded the resolution of the highresolution STIS and COS spectra. We also compared the SED to an ADS spectrum calculated with Teff = 18 600 K and log g = 3.15, which was reddened with E(B − V ) = 0.05 to test the effective temperature determined from the optical spectrum. Overall, good agreement is found, accept for some minor mismatches. Table 10.5.: Abundances determined from the UV of HD 271791 star CAa HD 271791 star CAa HD 271791

C 8.35 8.0 ± 0.09 V 3.96 -

N 7.77 7.50 Co 4.91 4.82 ± 0.08

Al 6.26 6.16 ± 0.04 Ti 4.91 4.74 ± 0.03

Si 7.46 7.21 ± 0.05 Mn 5.48 5.22 ± 0.12

Mg 7.40 7.15 ± 0.09 Ni 6.20 6.03 ± 0.10

Cr 5.64 5.43 ± 0.18 Cu 4.25 -

Fe 7.37 7.15 ± 0.11 Zn 4.63 4.35 ± 0.15

a

Present-day cosmic abundances (CA) from 63 mid B-type to late O-type stars (Irrgang in prep.). For the iron group solar abundances by Asplund et al. (2009) are taken.

To determine the abundances we took in a first step the few unblended lines to determine the abundances of C, Si, Mg and Fe. Based on these results we iteratively determined the

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10.4. THE SUPERNOVA SCENARIO

1e-11

-2

Flambda [erg/cm/s ]

1e-12

1e-13

1e-14

1e-15

1e-16

1e-17 1000

10000 lambda [Angstrom]

Figure 10.9.: SED of HD 271791 using COS spectra (black), high resolution STIS spectra (grey), lowresolution STIS (blue) and photometry of HD 271791 (blue squares).

abundances for the other elements from blended lines. The results can be found in Table 10.5. In Appendix E, we show the comparison of our model spectrum with the observations of HD 271791.

10.4. The supernova scenario: nucleosynthesis in a core-collapse supernova New discoveries of massive, very close binaries and new stellar evolution calculations show that the possible separation of the progenitor system of the runaway HD 271791 can be smaller than expected before. This leads to a higher possible ejection velocity. Therefore, the supernova scenario can explain the rest-frame velocity of HD 271791, assuming an ejection in direction of the Galactic rotation. Gvaramadze (2009) appears to be suited ledd to explain all observational data. The analysis of a higher-quality spectrum confirms the α−enhancement found before by Przybilla et al. (2008). However, to discriminate between different calculations for supernova yields, the systematic errors in the spectrum synthesis would need to be reduced significantly. The determination of the elements in the UV also confirms the findings of the abundance analysis in the optical. Due to the fact that almost all lines are blended in the UV, the abundance analysis is not so straightforward than in the sharp-lined stars. Large uncertainties are obtained in particular because several elements are analyzed in LTE, as more sophisticated NLTE model atoms are unavailable at the moment. Moreover, we could not derive abundances for all elements yet. This will, however, be done in the future by fitting several elements at once. The abundances in the iron-group are about 0.2 dex lower than found in the comparison stars. This coincides


166

with the iron abundance and was expected, as the runaway star has a lower metallicity due to its origin from the outskirts of the galaxy. As a next step, we will also determine the abundances of the trans-iron group elements, by comparing single lines of the runaway to the lines of our comparison star ι Her, but this is beyond the scope of this thesis.

11. Future work 11.1. Eclipsing hot subdwarf binaries – The EREBOS project Currently we know 17 HW Vir systems. Three of them have substellar companions. The known HW Vir systems have been discovered using different methods and the sample is therefore very inhomogeneous. However, to study the properties of the population of hot subdwarf stars with low-mass stellar or substellar companions, a large and homogeneously selected sample of eclipsing binaries is essential. Most recently, thirty-six new HW Vir candidates have been discovered by the OGLE project (Pietrukowicz et al. 2013; Soszynski et al. 2015), tripling the number of such objects and providing the first large and homogeneously selected sample of eclipsing sdB stars. The stars have been identified by their blue colours and their characteristic light curve shapes in the I-band. These light curve shapes and the derived orbital periods leave no doubt that those are indeed HW Vir systems. We already obtained time-resolved spectroscopy of two bright binaries from this sample with EFOSC2 and confirmed their HW Vir nature. Moreover, we got observing time with FORS2 on the VLT granted for two highly interesting short-period systems, which will be observed beginning of May 2015. To investigate this unique sample we start the EREBOS (Eclipsing Reflection Effect Binaries from the OGLE Survey) project that aims at measuring orbital and atmospheric parameters for all these systems. The most crucial part of the project is time-resolved spectroscopy of these rather faint and short-period binaries, because the individual exposure times must be short (∼ 5% of the orbital period) to prevent orbital smearing. Therefore, a large amount of observing time is required for the spectroscopic and photometric follow-up. Hence, we already proposed for a large filler programme for VLT/FORS2 stretched over 4 periods to obtain phase resolved spectroscopy of the 23 newly discovered HW Vir systems with orbital periods . 3 h and I-band magnitudes . 19.5. Moreover, we proposed for spectroscopic and photometric follow-up with several additional telescopes within our collaboration. This project will triple the number of well-studied HW Vir systems and due to the homogeneous selection it will allow us to study the population properties in a quantitative way for the first time. Due to the large fraction of substellar companions we found amongst the short period reflection effect binaries (see Sect 7.8), we expect up to 50% of all our systems to contain substellar companions. Five of the systems from the OGLE sample have orbital periods shorter than all the before known HW Vir systems. This means, we can systematically investigate the so far unstudied region at short periods shown in Fig. 7.20 where the least massive and closest companions might be located. By analysing the time-resolved spectroscopy together with the lightcurves we will be able to determine the masses of both components and the separation of the system. This means we will increase the number of eclipsing post common-envelope binaries with sdB and low mass companions with known system parameters, which will help for a better understanding of the very important, but not well understood common-envelope phase. Moreover, the determination of accurate system parameters (orbit, mass, radius) of a large number of reflection effect binaries will help us to understand the reflection better, which can not be modelled physically until now, but is only parametrized by the albedo of the companion. The discovery of the first HW Vir system with a BD companion containing a pulsating sdB

167

CHAPTER 11. FUTURE WORK

168

(Sect. 7.6) also opens new possibilities to study the role of substellar companions in the formation of sdB binaries. Asteroseismology allows an independent and accurate determination of the sdB mass. We already proposed for higher resolution spectroscopic and photometric follow-up time for this unique system with ESO-VLT/XSHOOTER and ESO-NTT/EFOSC2. This system could be a Rosetta stone for understanding sdB stars, their binary systems, their pulsations and the role of substellar companions. The photometric surveys already found a large number of new eclipsing sdB binaries and will find more in the future. Therefore, they will become certainly a milestone for the understanding of low-mass companions on the stellar evolution and the common envelope phase.

11.2. Spectrum synthesis in the UV and runaway stars The analysis of the four bright B stars of different temperatures and our tests showed that our spectrum synthesis in the UV works fine. We can now use it to determine the abundances of trans-iron elements in our runaway star, The finding of enhanced r-process abundances could prove core-collapse supernovae as sites of the r-process, which is debated upon (with merging binary neutron stars being an alternative site), but direct observational evidence is unavailable at the present.This will hopefully further confirm the origin of HD 271791 in a binary supernova scenario. Moreover, we want to apply for observing time with HST and analyze more candidate runaway stars from the SN scenario, already found by Irrgang (2014), to study nucleosynthesis in a core-collapse SN further. These systems give us the unique opportunity to put observational constraints on the yields produced in a supernova. W Furthermore, we will seek collaborations with supernova modelers to simulate the process taking place in binary supernovae in order to to minimize the assumptions made in the calculation of the accretion and mixing of the supernova ejecta. To minimize the error in the abundance analysis, we want to improve the synthetic model spectra by developing NLTE model atoms for iron-group elements, which give rise to most lines found in the UV. Furthermore, I want to perform a comprehensive abundance study of bright B stars study using UV spectra from the HST archive to get present-day cosmic abundances for iron-group and higher mass elements in the solar neighborhood. Quantitative spectroscopy of B stars in the UV to that extent has not been performed before. A comprehensive study of the abundances of the iron group and trans-iron group elements of bright B stars is unavailable so far. All studies done so far concentrated on small wavelength ranges and single lines.

Appendix A. Orbital parameters for known post common-envelope systems and their substellar companions Table A1.: Orbital parameters for the known eclipsing PCEBs (sdB/WD+dM) and reflection effect binaries (sdB+dM) (after Zorotovic & Schreiber 2013; For et al. 2010; Jeffery & Ramsay 2014), including the systems analyzed in this thesis. Systems with suspected planets are marked in bold (see Table A2) System

Alt. Name

Porb [d]

M1 [M ]

M2 [M ]

0.485 ±0.013 0.483 0.47: ∼ 0.46 0.459±0.005 0.48±0.03 0.376±0.055 0.5: ∼ 0.25 ∼ 0.47 0.461±0.051 0.471±0.005 0.45±0.17 – 0.48 ± 0.03 0.47 0.47 ± 0.03 0.47: 0.526 ± 0.05 – – – – – – – – – – 0.47:

0.142±0.004 0.134 0.075: ∼ 0.21 0.122±0.001 0.12±0.01 0.113±0.017 0.16: 0.045±0.03 0.068±0.03 0.157±0.017 0.0788+0.0075 −0.0063 0.12±0.05 – 0.064 ± 0.004 0.116 ± 0.007 0.069 ± 0.005 0.16 ± 0.05 0.174 ± 0.016 – – – – – – – – – – 0.12:

References

Reflection effect/ eclipsing binaries HW Vir HS 0705+6700 HS 2231+2441 NSVS 14256825 NY Vir 2M1938+4603 NSVS 07826247 BUL-SC16 335 SDSSJ0820+0008

2M J1244-0840 2M J0710+6655 2M J2234+2456 2M J2020+0437 PG 1336-018 NSVS 05629361 CSS06833 2M J1809-2641 GSC 0196.0617

ASAS 10232 AA Dor EC 10246-2707 FBS 0747+725 SDSSJ1622+4730 SDSSJ1922+372220 V2008-1753 BUL-SC 16 335 PTF1 J07245+1253 PTF1 J011302+2257 OGLE GD ECL 10384 OGLE GD ECL 09869 OGLE GD ECL 07446 OGLE GD ECL 11471 OGLE GD ECL 09426 OGLE GD ECL 11388 OGLE GD ECL 00586 OGLE GD ECL 00998 OGLE GD ECL 03782 OGLE GD ECL 08577

2M J1023-3736 LB 3459 VSX J075328.9+722424

0.11671955 0.095646625 0.110588 0.1103741 0.101015967 0.1257653 0.16177042 0.12505028 0.097 0.13927 0.261539736 0.118507993 0.2082535 0.0697885 0.168876 0.065817833 0.125050278 0.09977 0.0917 0.07753698 0.09596148 0.11659550 0.1208333 0.12980483 0.14780615 0.18660216 0.39802830 0.43537749 0.50660638

1,2 3, 4 5 6 7, 8, 9 10 11 12 15 15 16 17,18 19 37 41 33 40 70 39 42 38 38 38 38 38 38 38 38 38 38

reflection effect/non-eclipsing binaries PG 1017−086 HS 2333+3927 PG 1329+159

XY Sex Feige 81, PB 3963

0.073 0.1718023 0.249699

– 0.38 –

– 0.29 0.35a

20 21 22

XV

XVI

APPENDIX

Table A1.: Orbital parameters for the known eclipsing PCEBs (sdB/WD+dM) and reflection effect binaries (sdB+dM) (after Zorotovic & Schreiber 2013; For et al. 2010; Jeffery & Ramsay 2014), including the systems analyzed in this thesis. Systems with suspected planets are marked in bold (see Table A2) System

Alt. Name

2M 1926+3720 PG 1438−029 HE 0230−4323 JL 82 BPS CS 22169 FBS 0117+396 HS 2043+0615 UVEX J0328+5035 Feige 48 KIC 11179657 KIC 2991403 V1405 Ori B4 NGC6791 EQ Psc CPD−64◦ 481 PHL 457

KBS 13

KUV 04421+1416

Porb [d]

M1 [M ]

M2 [M ]

References

0.249702 0.2923 0.33579 0.4515 0.7371 0.1780 0.252 0.3016 0.11017 0.3438 0.3944 0.4431 0.398 0.3985 0.801 0.27736315 0.3131

– – – – – – – – – – – – – – – – –

– – – 0.30a 0.21a 0.19a – – – – – – – – – – –

23 24 23 25 26 27 28 29 30 31 32 32 34 35 36 43 43

0.13008014 0.52118343 0.1507575 0.30370363 0.364139315 0.344330833 0.52103562 0.332687 0.1344377 0.06509654 0.12448976 0.3358711 0.125631 0.1855177 0.08096625 0.363497 0.3820040 0.14943807 0.1565057 0.229120 0.2484 0.1949589 0.227856 0.3309896 0.13011232 0.15087074 0.1219587 0.3587 0.3861 0.4615 0.35046872

0.535±0.012 0.84±0.05 0.78±0.040 0.440±0.022 0.51+0.06 −0.02 0.564±0.014 0.554±0.017 0.47±0.02 0.878-0.946 0.51±0.05 0.415±0.010 0.439±0.002 0.48-0.53 0.614-0.678 0.350±0.081 0.470±0.055 0.410±0.024 0.370±0.018 0.37 0.370±0.016 0.590±0.017 – 0.400±0.026 0.520±0.026 0.390±0.035 0.430±0.025 – 0.51±0.09 0.65±0.11 0.52±0.05 0.61±0.04

0.111±0.004 0.93±0.07 0.430±0.040 0.183±0.013 0.41±0.06 0.116±0.003 0.555±0.023 0.255-0.380 0.224-0.282 0.09±0.01 0.158±0.006 0.273±0.002 0.190-0.246 0.146-0.201 – 0.380±0.012 0.255±0.040 0.319±0.061 – 0.196±0.043 0.319±0.061 – 0,319±0.061 0.319±0.061 0.255±0.040 0.431±0.108 – 0.35±0.05 0.35±0.05 0.35±0.05 0.39±0.03

44, 46, 48 49 50, 52 53 54 54 55 56 51 54 54 57, 58, 58, 57, 59 58, 58, 57 58, 57, 57, 57, 57 60 60 60 61

Detached WD+MS PCEBs NN Ser V471 Tau QS Vir RR Cae DE Cvn GK Vir RX J2130.6+4710 SDSSJ0110+1326 SDSSJ0303+0054 SDSSJ0857+0342 SDSSJ1210+3347 SDSSJ1212-0123 SDSSJ1435+3733 SDSSJ1548+4057 CSS06653 CSS07125 CSS080408 CSS080502 CSS09704 CSS09797 CSS21357 CSS21616 CSS25601 CSS38094 CSS40190 CSS41631 WD 1333+005 PTFEB11.441 PTFEB28.235 PTFEB28.852 KIC-10544976

2M J1552+1254 2M J0350+1714 EC 13471-1258 2M J0421-4839 RX J1326.9+4532 SDSSJ1415+0117 2M J2130+4710 WD 0107+131 CSS03170

SDSSJ1329+1230 SDSSJ1410-0202 SDSSJ1423+2409 SDSSJ0908+0604 SDSSJ2208-0115 SDSSJ1456+1611 SDSSJ1348+1834 SDSSJ1325+2338 SDSSJ1244+1017 SDSSJ0939+3258 SDSSJ0838+1914 SDSSJ0957+2342 SDSSJ1336+0017 PTF1 J004546.0+415030.0 PTF1 J015256.6+384413.4 PTF1 J015524.7+373153.8 USNO-B1.0 1377-0415424

45 47

51

58 59 59 58 59 59 59 58 58 58

XVII

A. ORBITAL PARAMETERS FOR KNOWN POST COMMON-ENVELOPE SYSTEMS

Table A1.: Orbital parameters for the known eclipsing PCEBs (sdB/WD+dM) and reflection effect binaries (sdB+dM) (after Zorotovic & Schreiber 2013; For et al. 2010; Jeffery & Ramsay 2014), including the systems analyzed in this thesis. Systems with suspected planets are marked in bold (see Table A2) System SDSS SDSS SDSS SDSS SDSS SDSS SDSS SDSS SDSS SDSS SDSS SDSS

Alt. Name

J0821+4559 J0927+3329 J0946+2030 J0957+3001 J1021+1744 J1028+0931 J1057+1307 J1223-0056 J1307+2156 J1408+2950 J1411+1028 J2235+1428

Porb [d]

M1 [M ]

M2 [M ]

References

0.50909 2.30822 0.252861219 1.92612 0.14035907 0.23502576 0.1251621 0.09007 0.216322132 0.1917902 0.167509 0.14445648

0.66±0.05 0.59±0.05 0.62±0.10 0.42±0.05 0.50±0.05 0.42±0.04 0.34±0.07 0.45±0.06 – 0.49±0.04 0.36±0.04 0.45±0.06

0.431±0.108 0.380±0.012 0.255±0.040 0.380±0.012 0.319±0.061 0.380±0.012 0.255±0.040 0.196±0.043 0.319±0.061 0.255±0.040 0.380±0.012 0.319±0.061

58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58,

0.08786542 0.08682041 0.06236286

∼ 0.71 0.80±0.04 1.2: 0.6:

∼ 0.14 0.18±0.06 0.14: 0.09:

63, 64 65, 66 67, 68 69

62 62 62 62 62 62 62 62 62 62 62 62

CVs UZ For HU Aqr DP Leo

2M J0335-2544 2M J2107-0517 RX J2107.9-0518

References. (1) Lee et al. (2009), (2) Beuermann et al. (2012b), (3) Drechsel et al. (2001), (4) Beuermann et al. (2012a), (5) Østensen et al. (2008), (6) Wils et al. (2007), (7) Vuˇcković et al. (2007), (8) Charpinet et al. (2008), (9) Qian et al. (2012b), (10) Østensen et al. (2010), (11) For et al. (2010), (12) Polubek et al. (2007), (14) Geier et al. (2011c), (16) Schaffenroth et al. (2013), (17) Kilkenny (2011), (18) Klepp & Rauch (2011), (19) Barlow et al. (2013), (20) Maxted et al. (2002), (21) Heber et al. (2004), (22) Maxted et al. (2004b), (23) Green et al. (2004), (24) For et al. (2008), (25) Koen (2007), (26) Koen (2009), (27) Edelmann et al. (2005), (28) Østensen et al. (2013), (29) Geier et al. (2014), (30) Kupfer et al. (2014), (31) Latour et al. (2014), (32) Kawaler et al. (2010), (33) Schaffenroth et al. (2014b), Sect 7.8, (34) Koen et al. (1999), (35) Pablo et al. (2011), (36) Jeffery & Ramsay (2014), (37) Pribulla et al. (2013) (38) Pietrukowicz et al. (2013), (39) Schindewolf et al., submitted, (40) Schaffenroth et al. (2015), Sect. 7.6, (41) Schaffenroth et al. (2014c), Sect. 7.4, (42) Kupfer priv. comm, (43) Schaffenroth et al. (2014a), Sect. 7.5, (44) Parsons et al. (2010a), (45) Beuermann et al. (2010), (46) O’Brien et al. (2001), (47) Kundra & Hric (2011), (48) O’Donoghue et al. (2003), (49) Maxted et al. (2007), (50) van den Besselaar et al. (2007), (51) Parsons et al. (2010b), (52) Parsons et al. (2012), (53) Maxted et al. (2004a), (54) Pyrzas et al. (2009), (55) Parsons et al. (2011), (56) Pyrzas et al. (2012), (57) Backhaus et al. (2012), (58) Rebassa-Mansergas et al. (2012), (59) Drake et al. (2010), (60) Law et al. (2012), (61) Almenara et al. (2012), (62) Parsons et al. (2013), (63) Bailey & Cropper (1991), (64) Potter et al. (2011), (65) Schwarz et al. (2009), (66) Schwope et al. (2011), (67) Pandel et al. (2002), (68) Beuermann et al. (2011), (69) Schwope et al. (2002), (70) Polubek et al. (2007), (a ) Geier et al. (2010) Notes: Very uncertain values are followed by “:”. It generally means that the mass was assumed and not derived.

XVIII

APPENDIX

Table A2.: Best fits of the orbital parameters for the currently claimed planets around eclipsing PCEBs.

Name

Msin(i) [Mj]

HW Vir c 14.3±1.0 HW Vir d 30-120 HS0705+6700 c 31.5±1.0 HS2231+2441 c 13.94±2.20 NSVS14256825 c 2.8±0.3 NSVS14256825 d 8.0±0.8 NY Vir c 2.78±0.19 NY Vir d 4.49±0.72: NN Ser c 6.91±0.54 NN Ser d 2.28±0.38 V471 Tau c 46-111 QS Vir c 9.01 QS Vir d 56.59 RR Cae c 4.2±0.4 UZ For c 6.3±1.5 UZ For d 7.7±1.2 HU Aqr c 7.1 DP Leo c 6.05±0.47

P [yr]

asin(i) [AU]

12.7±0.2 4.69±0.06 55±15 12.8±0.2 8.41±0.05 3.52 15.7 ∼ 5.16 3.49±0.21 1.9±0.3 6.86±0.25 2.9±0.6 8.18±0.18 3.39±0.19 27±3.7 7.56±0.64 15.50±0.45 5.38±0.20 7.75±0.35 3.39±0.10 33.2±0.2 ∼ 12.6 − 12.8 14.4 ∼ 6.32 16.99 ∼ 7.15 11.9±0.1 5.3±0.6 16+3 5.9±1.4 5.25±0.25 2.8±0.5 9.00±0.05 4.30 28.01±2.00 8.19±0.39

e 0.40±0.10 0.05: 0.38±0.05 – 0.00±0.08 0.52±0.06 – 0.44±0.17 0.0 0.20±0.02 0.26±0.02 0.62 0.92 0 0.04±0.05 0.05±0.05 0.13±0.04 0.39±0.13

Ref. 1 1 2 3 4 4 5 5 6 6 7 8 8 9 10 10 11 12

Notes

* *

* *

References. (1) Beuermann et al. (2012b), (2) Beuermann et al. (2012a), (3) Qian et al. (2012b), (4) Almeida et al. (2013), (5) Lee et al. (2014), (6) Beuermann et al. (2010), (7) Kundra & Hric (2011), (8) Almeida & Jablonski (2011), (9) Qian et al. (2012a), (10) Potter et al. (2011), (11) Go´zdziewski et al. (2012), (12) Beuermann et al. (2011) ∗ The claimed third body is more consistent with a BD than with a planet. Notes: Very uncertain values are followed by “:”.

XIX

B. ATOMIC DATA

B. Atomic Data All atomic data used to derive the synthetic spectra. The model atoms in Table A1 are used in Detail to derive the population numbers. Table A2 and A3 summarize the data used in Surface to calculate the final synthetic spectrum. Table A1.: Model atoms for NLTE calculations Ion H He I/II C II-IV N II O I/II Ne I/II Mg II Al II/III Si II-IV S II/III Ar I/II Fe II/III

Model atom Przybilla & Butler (2004) Przybilla (2005) Nieva & Przybilla (2006, 2008) Przybilla & Butler (2001) Przybilla et al. (2000); Becker & Butler (1988), updated Morel & Butler (2008), updated Przybilla et al. (2001) Przybilla (in prep.) Przybilla & Butler (in prep.) Vrancken et al. (1996), updated Butler (in prep.) Becker (1998); Morel et al. (2006), corrected Table A2.: Atomic Data for NLTE calculations

atomic number Z 6

element

7

N

8

O

12 13

Mg Al

14

Si

16

S

26

Fe

C

ionization stage I II III IV I II III I II III II II III II III IV II III II III IV

linelist 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,3 1,3 1,3

energy levels 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

collisional broadening 2,a c,2,a 2,a 2,a,d a c,2,a a 2,a c,2,a a,d a c,2,a a,d c,2,a 2,a d,2,a a,c a d,2,a 2,a 2,a

natural broadening b,2 b,2 b,2 b,2 b,2 b,2 b,2 b,2 b,2 b b b,2 b b,2 b,2 b,2 b,2 2 2 2 2

(1) NIST: Ralchenko (2005), http://www.nist.gov/pml/data/asd.cfm (2) Kurucz (2011), http://kurucz.harvard.edu/linelists/ (3) FERRUM project: Johansson et al. (2002) (a) formula by Cowley (1971) (b) Topbase: Cunto & Mendoza (1992), http://cdsweb.u-strasbg.fr/topbase/topbase.html (c) Griem (1974) (d) STARK-B: Sahal-Bréchot et al. (2014), http://stark-b.obspm.fr/

XX

APPENDIX

Table A3.: Atomic Data for LTE calculations atomic number Z 9

element

21

Sc

22

Ti

23

V

24

Cr

25

Mn

26

Fe

27

Co

28

Ni

29

Cu

30

Zn

31

32

Ga * * * * Ge

33

* * As

38

Sr

F

ionization stage I II III IV V VI III IV V VI III IV V IV III IV V VI III IV V VI V VI III IV V VI III IV V VI III IV III IV V II III IV V VI II III IV V VI II III IV II

linelist 2 2 2 2 2 2 2,3 2 2 2,3 2 2 2 2 2 2 2 2 2,3 2 2,3 2 2,3 2 2 2,3 2,3 2 2 2,3 2,3 2 4 4 2 5 5 6 6 7 7 7 2 8 8 9 9 8 8 8 2

energy levels 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

collisional broadening a a c,2 2 2 2 2 c,2 2 2 2 2 2 2 a 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 a a a a a a a a a a a a a a a a a a a

natural broadening b b 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 -

XXI

B. ATOMIC DATA

39

Y

40

Zr

41 42

44

Nb Mo * Tc * * * Ru

45

Rh

46

Pd

47

Ag

48 49

Cd In

50

Sn

51

Sb

52

Te

56

57

Ba * * * La

58

Ce

62 63

Sm * Eu

64

Gd

67 68 69 70

Ho Er Tm Yb

43

II III II III II II III II IV V VI II III II III II III II III II II III II III IV II III IV II III II V VI VII II III II III IV II III II III II III III III III II III IV

2 8 2 8 2 2 11 8 12 12 12 2 13 2 14 2 14 2 14 2 2 8 2 8 8 8 8 8 8 8 2 15 15 15 2 8 2 8 8 2 16 2 8 2 8 17,18 19 20 2 21 22

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

-

XXII

APPENDIX

71

Lu

72 74

Hf* W

75 76 77 78 79

* Re Os Ir Pt Au

80 81

Hg Tl

82

Pb

83

Bi

II III III II III IV II II II II II III II II III II III IV II III IV

2 8 26 2 21 25 2 2,23 2,24 8 8 8,27* 2 8 8 2 8 8 8 8 8

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

a a a a a a a a a a a a a a a a a a a a a

-

(1) NIST: Ralchenko (2005), http://www.nist.gov/pml/data/asd.cfm (2) Kurucz (2011), http://kurucz.harvard.edu/linelists/ (3) Iron project: Hummer et al. (1993), http://cdsweb.u-strasbg.fr/topbase/TheIP.html (4) Hirata & Horaguchi (1994), http://cdsarc.u-strasbg.fr/viz-bin/Cat?VI/69 (5) Rauch et al. (2014a), http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/A+A/564/A41 (6) Castelli & Parthasarathy (1995) (7) Rauch et al. (2015) (8) Morton (2000), http://iopscience.iop.org/0067-0049/130/2/403/fulltext/ (9) Rauch et al. (2012), http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/A+A/546/A55 (10) Nilsson et al. (2010) (11) Quinet (2015) (12) Werner et al. (2015), http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/A+A/574/A29 (13) Palmeri et al. (2009) (14) Zhang et al. (2013) (15) Rauch et al. (2014b), http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/A+A/566/A10 (16) Biémont et al. (2003) (17) Biémont et al. (2001c) (18) Zhang et al. (2002) (19) Biémont et al. (2001a) (20) Li et al. (2001) (21) Biémont et al. (2001b) (22) Wyart et al. (2001) (23) Quinet et al. (2006) (24) Xu et al. (2007) (25) Enzonga Yoca et al. (2012) (26) Malcheva et al. (2009) (27) Enzonga Yoca et al. (2008) (a) formula by Cowley (1971) (b) Topbase: Cunto & Mendoza (1992), http://cdsweb.u-strasbg.fr/topbase/topbase.html (c) STARK-B: Sahal-Bréchot et al. (2014), http://stark-b.obspm.fr/

XXIII

C. LINE DISTRIBUTION OF DIFFERENT ELEMENTS

C. Line distribution of different elements at different effective temperatures The following figures show the distributions from lines of different elements and ionization stages until the iron group over a wavelength from 1000 − 3000 ˚ A. Therefor we calculated synthetic spectra with our models. To illustrate the high dependence of the line distribution from the effective temperature of the star, the distribution was calculated for four different effective temperatures using the parameters of four different stars (see Table C1). The synthetic spectra were not broadened by macroscopic broadening mechanisms like rotation or macroturbulence, but only the natural broadening, pressure broadening and microturbulence.

star ι Her γ Peg HR 1861 τ Sco

Table C1.: Parameters used to calculate model spectra effective temperature [K] surface gravity [cgs] microturbulence [km s−1 ] 17500 3.85 2 21550 3.96 2 27000 4.18 4 31650 4.30 4

APPENDIX

relative Flux

relative Flux

relative Flux

relative Flux

CI/II/III/IV: Iota Her

1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000 XXIV

XXV

relative Flux relative Flux

1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

CI/II/III/IV: Gamma Peg

APPENDIX

relative Flux

relative Flux

relative Flux

relative Flux

CI/II/III/IV: HR 1861

1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2200

2400

2600

2800

3000 XXVI

2000 λ [Å]

XXVII


1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

CI/II/III/IV: Tau Sco

APPENDIX

relative Flux

relative Flux

relative Flux

NI/II/III: Iota Her

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XXVIII

XXIX

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

NI/II/III: Gamma Peg

APPENDIX

relative Flux

relative Flux

relative Flux

NI/II/III: HR 1861

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XXX

XXXI

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

NI/II/III: Tau Sco

APPENDIX

relative Flux

relative Flux

relative Flux

OI/II/III: Iota Her

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XXXII

XXXIII

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

OI/II/III: Gamma Peg

APPENDIX

relative Flux

relative Flux

relative Flux

OI/II/III: HR 1861

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XXXIV

XXXV

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

OI/II/III: Tau Sco

APPENDIX

relative Flux

MgII: Iota Her

1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

2400

2600

2800

3000

relative Flux

MgII: Gamma Peg

1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

XXXVI

XXXVII

relative Flux

MgII: HR 1861

1 0.5

1200

1400

1600

1800

2000 λ [Å]

2400

2600

2800

3000

2200

2400

2600

2800

3000

relative Flux

MgII: Tau Sco

1 0.5

1200

1400

1600

1800

2000 λ [Å]


2200

APPENDIX

relative Flux

relative Flux

AlII/III: Iota Her

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XXXVIII

XXXIX

relative Flux

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

AlII/III: Gamma Peg

APPENDIX

relative Flux

relative Flux

AlII/III: HR 1861

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XL

XLI

relative Flux

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

AlII/III: Tau Sco

APPENDIX

relative Flux

relative Flux

relative Flux

SiII/III/IV: Iota Her

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XLII

XLIII

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

SiII/III/IV: Gamma Peg

APPENDIX

relative Flux

relative Flux

relative Flux

SiII/III/IV: HR 1861

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XLIV

XLV

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

SiII/III/IV: Tau Sco

APPENDIX

relative Flux

relative Flux

SII/III: Iota Her

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XLVI

XLVII

relative Flux

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

SII/III: Gamma Peg

APPENDIX

relative Flux

relative Flux

SII/III: HR 1861

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

XLVIII

XLIX

relative Flux

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

SII/III: Tau Sco

APPENDIX

relative Flux

relative Flux

relative Flux

ScII/III/IV: Iota Her

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

L

LI

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

ScII/III/IV: Gamma Peg

APPENDIX

relative Flux

relative Flux

relative Flux

ScII/III/IV: HR 1861

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

LII

LIII

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

ScII/III/IV: Tau Sco

APPENDIX

relative Flux

relative Flux

relative Flux

relative Flux

TiII/III/IV/V: Iota Her

1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000 LIV

LV


1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

TiII/III/IV/V: Gamma Peg

APPENDIX

relative Flux

relative Flux

relative Flux

relative Flux

TiII/III/IV/V: HR 1861

1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000 LVI

LVII


1 0.5 1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

TiII/III/IV/V: Tau Sco

relative Flux relative Flux relative Flux relative Flux

1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LVIII

relative Flux

APPENDIX

VII/III/IV/V/VI: Iota Her

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LIX

VII/III/IV/V/VI: Gamma Peg

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LX

relative Flux

APPENDIX

VII/III/IV/V/VI: HR 1861

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXI

VII/III/IV/V/VI: Tau Sco

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXII

relative Flux

APPENDIX

CrII/III/IV/V/VI: Iota Her

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXIII

CrII/III/IV/V/VI: Gamma Peg

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXIV

relative Flux

APPENDIX

CrII/III/IV/V/VI: HR 1861

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXV

CrII/III/IV/V/VI: Tau Sco

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXVI

relative Flux

APPENDIX

MnII/III/IV/V/VI: Iota Her

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXVII

MnII/III/IV/V/VI: Gamma Peg

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXVIII

relative Flux

APPENDIX

MnII/III/IV/V/VI: HR 1861

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXIX

MnII/III/IV/V/VI: Tau Sco

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXX

relative Flux

APPENDIX

FeII/III/IV/V/VI: Iota Her

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXXI

FeII/III/IV/V/VI: Gamma Peg

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXXII

relative Flux

APPENDIX

FeII/III/IV/V/VI: HR 1861

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXXIII

FeII/III/IV/V/VI: Tau Sco

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXXIV

relative Flux

APPENDIX

CoII/III/IV/V/VI: Iota Her

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXXV

CoII/III/IV/V/VI: Gamma Peg

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXXVI

relative Flux

APPENDIX

CoII/III/IV/V/VI: HR 1861

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXXVII

CoII/III/IV/V/VI: Tau Sco

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXXVIII

relative Flux

APPENDIX

NiII/III/IV/V/VI: Iota Her

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXXIX

NiII/III/IV/V/VI: Gamma Peg

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5 1 0.5 1 0.5 1 0.5

LXXX

relative Flux

APPENDIX

NiII/III/IV/V/VI: HR 1861

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


1 0.5 1 0.5


relative Flux

LXXXI

NiII/III/IV/V/VI: Tau Sco

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

APPENDIX

relative Flux

relative Flux

CuII/III: Iota Her

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

LXXXII

LXXXIII

relative Flux

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

CuII/III: Gamma Peg

APPENDIX

relative Flux

relative Flux

CuII/III: HR 1861

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

LXXXIV

LXXXV

relative Flux

1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

CuII/III: Tau Sco

APPENDIX

relative Flux

relative Flux

relative Flux

ZnIII/IV/V: Iota Her

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

LXXXVI

LXXXVII

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

ZnIII/IV/V: Gamma Peg

APPENDIX

relative Flux

relative Flux

relative Flux

ZnIII/IV/V: HR 1861

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000

LXXXVIII

LXXXIX

relative Flux

1 0.5 1 0.5 1 0.5

1200

1400

1600

1800

2000 λ [Å]

2200

2400

2600

2800

3000


relative Flux

relative Flux

ZnIII/IV/V: Tau Sco

APPENDIX

XC

D. UV spectrum of ι Her Comparison of the HST/STIS observations of ι Her (black) with a synthetic model spectrum (red) calculated with ADS for the parameters of ι Her determined in Sect. 9.2 and summarized in Table 9.1 and 9.2.

Flux [erg s−1 cm−2 Å−1 ]

1160 1161

3.5×10-9

1162 1148

1163 1164 1149

1165 1150

1166 1167

1151

1168

1152

1169

1153

1170 λ [Å] 1171

1154

1172

1155

1173

1156

1174 1175

1157

1176

1158

1177 1178

FFe eI MFe IIIII n III II MF I Men n IIII IIIII

1147

Fe Si I MFNeiIIIII I Fen IIIIII I I N II iI N I i N II iI I Fe Fe II I SSFie I i IIIII III M C CrnII IIIIII FF I MCeeIIII n IIII C II FCFeeII I I FCFeIIIIII Fee I IIIIII II FCFeeI N IIIIII FN I I MFe II Feen IIIII N IIIII iII I M n FNe III I S III M MSiinII nII I F IIIII MFe II Nen I i IIIII III

1146

V M I M nIIII n FN Nei IIII F CVei IIIII rIIII MN n II I MF III Nen I N NFiei IIIII N FSei iIIIIIII I CFe IIIII r II FFe III e III II MC FCNenI I CNiIIIIIIII M IIII FFene I I VFS IIIIIII VFeeIIIIII I I I I Fe IIII FFe I FFSee IIIIII FNeeIII II i IIIIII II Fe I CSN III Fre IIIII Fe I I I FNe IIII Fei I CFFSeeIIIIIIIII r II N III FN N II CFe III Free II I III CVFFeI I VFreIII FeeIIIIII I C IIII r N C IIII rI CF II CFFNreeiII re IIII N CFFeIIIII re III II Fe III Fe I I NN IIII VNi II Ii II II FFee IIIII

FFee FSei IIIIII IIII I V II I Fe CF III Sre I Fei IIIIIII Fe III M VFFe IIII n FNeeIi IIIIIII Fe I II II CAFel II rI VNiIIIII IIII I

1145 1159

1×10-9

0.5×10-9

10 0

5

-5 0

-10

1179 1180

D. UV SPECTRUM OF ι HER

1.5×10-9

χ


V I C II CI I Fe C III CI FFSCe I FFCeeieIIIII Fe IIIIII NC III Ci IIII I FNCei I C IIII C VFNei II I MFC CI II C en IIII rI Fe IIIIIII FFe I Fee IIIIII I CFFNei IIII re I VFe IIII IIII I

V I Fe II Fe II III M n CF II re I F IIIII CVF e II re FeIIIII III F Ce r III CO III r FFeIIII Fee II II I C IIIII r V V IIII I I I CFNei II Fr I MFFeeeIIIII n I I I V IIIIII II I Si I V III II I C Vr MFeIIIII nI C IIIIII FCre I I Si IIIII FFC CI NCee IIIIII N i IIIIII iI VFC III FCeeII IIVI SCi II I

CSS r FSSeiiii IIIIII III Fe IIIIII Fe II I F MSieIII nI C IIIII rI I I FFe I eI M CFn IIIII M rneI III Fe IIIII I VNi II FFeIIII Fee IIII N III iI I N FFFeei II FNee IIIIII FFei IIII e IIIII II Fe I Fe II III Fe V II II I FFe e III F I V e II I Fe II II I MF One IIIII I VF eIIII I VFF I eeIIII IIII F FFeee I Fe IIIIII FOe II Fe I II V IIIIII I FFee II VF III eIIIIII II

XCI

χ

3.5×10-9

3×10-9

2.5×10-9

2×10-9

1.5×10-9

1×10-9

0.5×10-9

10 0

5

-5 0

-10

λ [Å]

1160

3×10-9

2.5×10-9

2×10-9


1196 1198 1200 1202 1204 1185

1206

1186

1208

1187

1210

1188

1212 λ [Å] 1214

1189

1216 1218

MF Vne II II I I Fe M F CFene III r IIII IIII CNFei r Fe III Si IIIII I FS II M Feeni III I C IIIIII MVr II MnII I Sn III VFFNSeeii III II N FeiiIIIIIIIIIII M III Sn I M CNni IIIII M FrenII C I CFN rreIIIIIIIIII Fe IIIIIII FFNNe II Mei III I C n IIII CSSSriii III I r III NIIIII FNSei I I M ni I FNe IIIII II M I C i CFSSN rreni IIII MFSN Nnei IIIIIIIIIIII I CSi II Fre IIII III I

1184

I

1183

I

1182

II

1181

Fe I

1180

V

MF en Fe IIII I CM I rn C CSFreIII MFrieIIIIIII nI I M II M CFSn I M FFreneei IIIIII nIIIIIII I Fe I MCSFioeIII VFn IIII MFFeeIIIIII ne MFFee IIIII n I FFNee IIIII IIIIII FN I CFee II r FNIIII FSeI II I CM CFFrenIIII FreeeIIII S III CS IIIIII VrIII C IIIII Cr I I Vr IIII II I I CF re I V II FI C e IIII Cr I r CFeIIIII rI FN NeiIIIIIII Ni II CFei II FreIII CFFNi III M SreneIII FFei IIIIII I C CVre IIIIII CrIIII I V CSri IIIII r IIIIIII Fe III F MFee IIII CFen I I Mr IIIIIIIIII CFANn I TreiliIII FeIIIIIIIII II FAe I lI MF III en S II C i IIIIII r Fe III III I VFSFAel NieIIIII i V IIIIII II CFF I FreeeIIII IIIIII Fe II Fe II I

χ

Flux [erg s−1 cm−2 Å−1 ] 2×10-9

1190 1191

1220

1192

1222

1193

1224

1194

1226 1228

A lI I FSeII Si III N C i II r I II II Fe NI N III I FNei I F I VFee II IIII M II An Cl I C IIIII FreI II SSFie III M inIIII M I n MC IIIII Fn I II CFee I II MFFre IIIIII en IIIIII III C II Fe I C TFSi III CCieIIIII r Fe IIII I C C IIII C I rI I CSC CrI I I I CIIII C CFSC II SCreiIIII I FCe III III

M Fen IIII I FCe I I CN CI AI FFFCNeel II e IIIIIIII FCNe IIII C II II

Fe I N N iIIII III I C rI M I Cn I r Fe IIIIII FFe I e IIIII III FFe e III FFee III M IIII Fne I II M II n CF II re I I IIII I VFNe FeIi IIII I Fe III CF III r C F e MFoeIII I CNne IIIII M FrneiIIII II I II

Fe N II i Fe II I Fe I FFe III Fee II Fe IIIIII N III iII I F Fee I I I CN II CriII r I F III Se I Fei III N II i III I FFe e III II M I n I N N I II IIII I MF en I Fe III IIII Fe MFe II nI III I

APPENDIX

χ

2.5×10-9

1.5×10-9

1×10-9

0.5×10-9

10 0

5

-5 0

-10

λ [Å]

1195

2×10-9

1.5×10-9

1×10-9

0.5×10-9

10 0

5

-5 0

-10

XCII

1230

χ


1250 1251 1252 1253 1254 1255 1256 1257 1258

1239

1259

1240 λ [Å]

1260 λ [Å]

1241

1261

1242

1262

1243

1263

1244

1264

1245

1265

1246

1266

I

1238 1247

1267

CZ Crn I Nr IIIIIII iI I Fe II II M CFFFene re II II CFe IIII r II III NF ieI IIII

1237

Fe I

1236

CF VFreeIIII II I I CV FreII IIII C Cr rI M IIIII n I Si I II S FF i C ee IIIII Fre IIII Fe III F III FFeee II C C o IIVI CFFre III FreeIIIII IIII CF I FFreeII e IIIIII II

1235

M CFe rnII IIIIII I CF r FeeIII M IIII Cn M CFSrnIIIII Cre III CMr IIIIIII un II III II FSe Fei IIII I C II MFe I C n I C II C I II I C CI I C r CFFeIII CFre I C CrreIIIIIIIIII ZNrn IIIIII iI I II

1234

MV nII II M II n II I

1233

M n CFe II C II MFC C enIIIIIII r IIIII IIII

1232

Z CMn rnIII III FFSee I V IIIVI FeIII MFe III nI C III r A III M l II MAn I n II FleIIIIIII II

1231

V FI M C en III r III C IIIII r N III iI I

Si Fe II CNSSi IIII Mri III n I II S Fei I C III rI II

1230 1248

1268

1249

0.5×10-9

10 0

5

-5 0

-10

1269 1270


1×10-9

χ


M g I F I M FeegII III

MSi I CV rgI II IIIII I

Si N II iI II C II I CFe rI IVI

u II I Fe II C CFr I re III II M n M III n C II rI I II

C

iI I N I FNe II C III rI II

N

Fe N II iI I

M Feg I III I

FNei IIII

N FieI I C III rI II M n I M II n II I

Ti Fe I IIII I

II M n M TSiinI II IIII I M Mn n II I M Cn I r FTei IIIII Fe III IIII

M n

V II I C Nr I iI N I i FNSe III Fei IIIII I CM Nr II FeinIII I S III II I

MC I nI C II I I FFFNe I CNee IIIIIIII r FeiIIIII III S CSii II FreIII IIII CFe r III III

XCIII

2×10-9

1.5×10-9

1×10-9

0.5×10-9

10 0

5

-5 0

-10

1250

2×10-9

1.5×10-9


1290 1291 1292 1293 1274

1294 1275

1295 1276

1296

1277

1297

1278

1298

1279

1299

1280 λ [Å]

1300 λ [Å]

II ZFFnee III I Fe IIII I FFee II O III C IIII o I C I Fre II III I SFFi ZneeIIIIIII III I N iI II FFFSei ee IIIII ZNni IIIIII I FOe IIII CFe II r I II N II iI Si II I Fe I II CVO I I rII CFFe IIII FreeI I M CFegIIIIII o C IIII o II ZFne IIII I F Me II g I II M g II C I I N Fei II III CSi r III M S CF ig I reIIII I FSei IIIII III I

1273

II

1272

Si I

1271

Si I

1270

VFe FeI II II Zn TTi II iI I S IIII TVSiii IIII II I V IIIIII F II Ce II o I I N I FFNee II IIII I

Zn C Fe II III V NI i III V II CrIII r III CF III r Ve II CTF II I M TFreiineI I M CN Vrni IIIIIIIIIII IIIIII II ZFFee n III Fe III Fe II V II II I TFei IIII CFFF I M r FCeeenoeIIIIII IIIIIII I C rI II FS TTFeeii III VFi IIIIIIIIIII eIIIII I Zn FCe II I F oI Ve IIII TCFioIIIII eIII F NF e II CFeieIII FFC FeeeIIIIIIIIII II Si IIII II I C o II

χ


0.5×10-9

10 0

5

-5 0

-10

1281

1301

1282

1302

1283

1303

1284

1304

I

1285 1286

1305 1306

1287

1307

1288

1308

C MV I MCnII n III III Fe I TFi II V eII N iIIIII C II rI II

II

CNi I r III I M I n Ti II I I N II iI I CNFie r IIII IIII M n I M II n M C n III FVre III IIIIIIII I

Fe CNi III Fre IIII I FCe III I MC III Cn II II CC r II C II SC I NFCi III I CieIII III CC I o II

F MFee I Fne III IV NFe IIII CM M Fi III FuneegIIIII IIII Fe III C II CFr I ZM oeg I Fne IIIIIIIII CFe I I o III I NF CMiegIIII r I II III FFe C Cre III r M I F IIIIII CFegIIIII r Fee III I IIII FCe II F Ce I r N ZniIIIIIII Fe I I IIII N iI FFee II Fe IIIII II FMFFeee I M nIIIII Znn III I IIII C I Fe I C CFe IIIII o I CMn II r C C CIIIIII Si I I CII CFC oe I I CC III Cr II II

F Tei II Ti II I II Fe II N III C i III r N Vi III V IIIIII M III Fn I Ve IIII II I I

1×10-9

M n

1.5×10-9

1289

1309

XCIV

1310

APPENDIX

χ

2×10-9

1290

2×10-9

1.5×10-9

1×10-9

0.5×10-9

10 0

5

-5 0

-10


1330 1331

2×10-9

1332 1333 II

II

1334 1335 1336 1337 1338 1339 1340 λ [Å] 1341 1342

1323

1343 1344

II

1322 1324

Fe FFe II Ne I i FNei IVIIII N IIIII iI Fe V M III n II S I NFei II iI Fe II II M n II I FFee IIII N I i S II NSii II i III III NFe iI II Fe II

1321

iI

1320 λ [Å]

N

1319

M ZFSSnn I ei I Sii IIIIIIIII III I F Me I I n Fe I I IIII

1318

NFe NSS i IIIII ii I I IIII I Fe II NS ii I FFSSSeiii IIIIII e IIIIIIIIII IIII

1317

II NFFFe ieeI IIIIII I Fe II I

1316

Ti I

1315

Fe FFe I I Fee IIIIII III I F Zne I NN III ii I II IIVI

1314

C II N Ni I Vi IIII FFNeIi I I FFe IIII NFeee IIIIIIII Ci I II CZC IIIII rn II I FFe I eI II Fe IV II FFee N IIII iI I II N Fei II III I

iI

Fe I

1313

N

I

1312

II

1311

M n

I Fe I Fe I IIII Fe I I Fe II CNi II Vr III I C IIIII rI II V FeIII I C II rI V

Fe I

1310 1325

1345

1326

1346

1327

1347

1328

1348

1329

0.5×10-9

10 0

5

-5 0

-10

1349 1350


1×10-9

χ


NFFNe ei II Fe IIIII Si II CFe IIII Fre II IIIIII I TFSei C i IIIIIII r I VNI I N IIIIII iI I Z Cn I r III Fe III SCi I I II VFC I I CeII FeIIIIIIII II C I TNFii II e IIIII VI

Fe VNi II IIII Fe I II FNei C III o I II C o II ZFNn I Fee IIIII III I N FFCeo I e II FFee IIIIII I Fe IIII Fe III CFe II r III II NF ei III C III r N II iI I II N iI II CFe r II I CFe III CFr II reIIII Zn IIII I Fe II C I C C C IIIII III Fe I CNi II r II I Fe III FNei III Fe IIVI II Fe II I Fe II N III Fei II III I

C Fre I Fe III III Fe II Fe I IIII I C Fre II Fe I I CFCeo IIIII Fre IIII Fe IIIIII Fe III CI I M CFCno III Fre I C e IIIIIIIII FreII I III

FFe eI V IIII II I

CF reI III I FNe III FNe CCFoe III r II FCIIIIII Ne III FieI I I C III Co I II M n NF III SiieIII IIII I

XCV

χ

2×10-9

1.5×10-9

1×10-9

0.5×10-9

10 0

5

-5 0

-10

1330

1.5×10-9


1350

1390 1351

1391 1352

1392 1353

1393 1354

1394 1355

1395 1356

1396

1357

1397

1358

1398

1359

1399

1360 λ [Å]

2×10-9

1400 λ [Å]

N iI Fe II II Fe I II Fe II N I Ci I r I Si IIII C IV NFreII FFei II I Fee IIII IIIIII I S C iI Cr I I FSoe IIII i IIII I S Fei II II I Fe MN III CFni Nre IIIII i N IIIIIII i FeIII N II Ni I I I iI V II II I Fe Fe I IIII I NFe I Fi FNFeeIIIIIII ei II NF I III Nei I i III II CFFe reII CCo IIIII CFFre III r I NFFSee IIIIII FFeeiei II I FCFe IIIIIIII oe I M IIIII n CN II M NSrnii III i IIVII III

Fe N III Ni I I iI I C II rI II C rI I C I r Fe III Fe III FFee III N IIIII FFei II e IIII Fe III NFe II i FFNeeIII FFei III II e NF IIIIII i I FSeei IIIIII IIVI F I Ne I I NFei IIII iI I II NF ZFneei II III Fe I FNe II i IIIII FFe II Fe IIII NFFee IIII ei IIII I Fe III FSe II NI I FFei IIII FSei I I CN NFreei IIIIIII iI N IIIIII iI I F VF e I NFFNeIIIIII eieiIIIII C IIIII Nr I i I F II V e IV NIIII iI I Fe FNei II I N IIII C i II rI I Fe II I Fe II II CNi r III III

χ


FASei N l III iI Fe IVIII FSei III Si I II IIII

Fe M II n CFFNe III M CNreniIIII rI M C ni IIIIIIII FreII I II Si IIII II N I iI I NFSFeie ZVFn IIIIII eII II NFe II Fei IIIII Fe III NI i I NFFSSeii IVI NNe IIIIIIIII ii II Fe IIIIII FFee IIII I ZFCne IIIII Fe III N IIII F M ei II Fn III F e IIII Te I I Ni IIII M CSSini I I NSrii III II M IIIIIII ZFneg I I C III r N III i TF II MFeieIII I n IIII II Fe II ZFne II FSFNei iIII M e IIIIII g II VFe II I M III FgI ZCneu III F M CFne IIIIII VreIIII TFi IIIIIIII CFeI I re I IIIII FFee I IIII FFee I III MM II MNSingII I CVFNni IIIIII reIiIIIII I NFe IIII i II III

ZCn Zn IIII II I

Si F FFeeeIIII FSei IIIIII II I C IIII FNe I i F IIVII FFee II e III II FFe e III N CCi III r VI N IIII iI I N NFie VF i IIII eIIIIIIII II V I N I Ci III MNFFeu I I FnieeIIIIII IIIIII

N NNiiI i II III Fe II N I Ni I I iI I I Fe I FSei II A Al IIII lI VFFeeIIIII IIII N II Ni I I i I S II Sii III FeIII ZNFn II SCeii II SFi IIIIIIIIII eI F CFe II reIII IIIII

2×10-9

1.8×10-9

1.6×10-9

1.4×10-9

1361

1401

1362

1402

1363

1403

1364

1404

1365

1405

1366

1406

1367

1407

1368

1408

1369

1409

XCVI

1410

APPENDIX

χ

2.2×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

0.2×10-9

10

5

-5 0

-10

1370

1.8×10-9

1.6×10-9

1.4×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

0.2×10-9

10

5

-5 0

-10

χ


1430 1431 1432 1433 1414

1434 1415

1435 1416

1.8×10-9

1436

1417

1437

1418

1438

1419

1439

1420 λ [Å]

1440 λ [Å]

1421

1441

1422

1442

1423

1443

1424

1444

1425

1445

1426

1446

1427

1447

C N o II i FFeIII e Fe IIII Fe III M III n II I Fe II

1413

FFe C e IIIII rI I CFe II CFNreiIIIII Nr IIIIII Fei IIIIII II CN I r C i IIIII rI I II

1412

Fe Fe I III Fe I Fe II FFee II N IIIII i FeIII II N FieI NF III FFeieI I Fee IIIII Fe IIIIIII Fe II III FFFee I I Fee IIIII I Fe IIII FCFee III o IIII III N Fei II IV N i FFe II Ne I I i IIIII NF II CieIIIII o II

1411

iI II Fe II I Fe N III NFei II NF i III i FeeIIII CSi III o I Si II Fe II II Fe I II

1410

N

F CNNFei II FFoeieIIIIIII CNFFeei IIVIIII Noe IIVI II MFi IIIV NFFFene I II i NNeieIIIIIIIII iI I CFFe IIVI NFFoe I eei IIIIIIII II C VI Cro I u II CZF IIIIII rne I Fe IIIII NFFe III ei IIIII FFFeee III Fe IIIIII Fe III F II NFe III NFeieII I Ni IIIII i IIIII II NF CNFeei I oI Sii IIIIIIIII S II Fei III F II NFe I ieI II IIII CNi Foe III N III Sii IIII II I CSi I Foe III FFee III IIIIII I

χ


1428

1448

1429

1449

N

iI

II

NFFei Ne IIII F i I II NFFFeee IIIII ieIIIII IIIII

F NFFNeeei II i II NFe IIII Ni I Fei IIII Fe III FFe III Fee I I N IIIIIII Ni I i I FFeIII NFNei IIIII ei IIII I F I Fe N NFFFeeieeIIIII F i IIIII CFFee IIIIIII re I N IIIIII NFiieII NFNiIIIII NFieIIIIIII ieI I IIII C rI II FFFee e III NS IIII Nii II i S IIIII Ni II I FNieI I CV i IIIII NFFSreII I Neii IIII Fi IIIIIIII NFFe III eieI IIII NFFee i II F II Ne I I iII II NFFee CNi IIII ri I F III N e IVI Tii III II NFFe II N Teii III FeIIIII Fe I I I F II CN e II NFrieII i II Fe IVI Ti II Ti II III F I Ne I Fi I I CTei IIII FreIII I IIIII NFe Fei II II NNi II i N IIIII iI N II N ii I IIII FFe I Tie I N III FieIII N IIII Fi NCSFFeeIIII ioeIII I MN III ni IIII II F Fee IV Fe I III NF IVI i FeeIIIVI N NCi III Ni IIIVI i IIIII II C rI MFFe II FFeen III FFNeei IIIIVIII e IIVV IVI CFFe N CNFeieIIIIII ui II III

S NF i II N Neii IIII Ni I I I i III I Fe I N N NiiIIIII i IIII I FNFeie I II I N IIV iI I I CN NNoi I I iI N IIIII iI II

2×10-9

1×10-9

0.8×10-9

0.6×10-9 10

5

-5 0

-10

1450


1.2×10-9

XCVII

1.8×10-9

1.6×10-9

1.4×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

0.2×10-9

10

5

-5 0

-10

1430

1.6×10-9

1.4×10-9


1470 1471 1452

1472 1453

1473 1454

1474 1455

1475 1456

1476

1457

1477

1458

1478

1459

1479

1460 λ [Å]

1480 λ [Å]

1461

1481

1462

1.8×10-9

1482

1463

1483

1464

1484

1465

1485

1466

1486

1467

1487

N NF i II ei III III Fe II N I Fei II II C II II M ZFFCnn eeIIIIII I NFFe III Cei IIV IIII

1451

Fe CF III M F oenI NFe III C ei IIII u II II I

1450

M F NFFFeegII FeeieIIII III FFFee IVII e II M Fe IIIIII nI I C I FFue I Ne III i IIIII Fe III II I FSei I Si I I I I FFSei III FSeei IIIIII NF III ei II III I

Fe FF I F ee II Fee IIII I NF IVI ie Fe IIIII FFe III Fee IIIII II NF II Feei III II CFFFe I oee II F IIIIII Ce II u I M II n C II o Fe II F I II ZFne IV e II IIII NFe I iII NF II Sei I F i IIIIII NF e III VFSeii III eIIIII III FFSei Ne III F i IIIII Ce IIII Foe II C FFo IIII Mee IIII g II Fe II FFe III Fee I C o IIIIIII FSe III i Fe III N II iII FFe I e III N I i M III Feg I CNFei IIII o III II Fe II I Fe I VFe II II II Fe II I Fe Fe III Fe II I M C gIII o F IIII Fee I CF IIII u I Fee IIIII I CC IIII o II I FFe Ne II i IIII II

χ

Flux [erg s−1 cm−2 Å−1 ] 1.6×10-9

1.4×10-9

1468

1488

1469

1489 1490

XCVIII

-10

NFFe I N ie I Ci IIIIIIII N II Ni I I iI I II Zn N II iI I M II N n II iI I Fe I Fe II II N I Fi I NFee IIII i IIII II C I FFeo I Fee IIII Fe IIII III Fe I FFee III I N III FCei I I II C III NFNoei I iI III M III C n II Fo I e Fe IIII FFFeee IIIII Fe IIII CF IIII FFoe I I Fee IIIIIII FFee III IIIII C I NFFeo II ie I IIII I

Fe Fe II II F I Ne I FieI II IIII

N Ni I i III I TFei IIII II NF Teii I C IIIIIII Feo I I III I N iI F Fee II Zn IIII Fe III II I I NFSei i NFFe IIIIII i Ne IIII i FeIIIII NF II eei II IIII CNi III r III II Fe I MNF i III enII FC IIIIII FFee IIII e IIII VII N iI II N F i II NFFee IIII Nei IIVI Ni I I i I Fe IIII I C II o II

Fe Fe IV II I N Fei I IIII NFe I I FieI II IIII

NFe i III Ti III NFF IV eieIII N IIIII iI V

NF ie F III N TTFFeeii I II i IIIIIIII e N IIIII N Feii III I IIIII I

APPENDIX

χ

1.8×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

10

5

-5 0

-10

1470

1.6×10-9

1.4×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

10

5

-5 0


1.6×10-9

1510 1511 1512 1513 1514 1515 1516

1497

1517

1498

1518

1499

1519

1500 λ [Å]

1520 λ [Å]

1501

1521

1502

1522

1503

1523

II V

1496 1504

1524

Fe F I NFee IIII Ni I I FFFei IIII ee II I III FNei III I FFe VII CFFee III r II CFe IIIIIIIII M FreenIII I II FFFe IVIII ee II FFFee IIIIII Sei IIII I F IV e III NFe II MFFei I FFFFenee IIII Nee IIIII FF i IIIIIIIIII CFFFeeee IIIII oe IIIII I Fe IIII Fe III CF Cre IIIII rI I Fe II Fe I Fe III N IIII iI I II FFe e I Fe IIII Fe III III I

1495

Fe I

1494

M Fn I Fee IIII I C II rI I FFee I IIII I

1493

II Fe Fe III II I

1492

Fe I

1491

F Ne II iI I II Fe I N II i FNe III Fei II IVII I

Fe FFFee II Ne IIII FFFeei IIIIII Fee IIIIIII FFe II Fee IIIIIIII II FFe III e FNFee IIIIII I NFFSi IIIII M CFFeeiei IIIIII FFreeen IIIIIIII IIIII Fe IIIIII Fe II FFee III FFee III e IIIIIIIII I FFe II e FFFee IIIII I e FFee IIIIII Fe IIII I FSei IIIIII FFe IIIII e II F e IIII FFFC Ceee IIIIIII Fe I IIII FFe II e III Fe IIII Fe I Fe III FFe III I ZFFne IIIIII NFFee I eieIIIIII I I IIII FFFeee I I FFFee IIIIIII Fee IIIIII Fe IIII Fe III I FFSei IIIII e II FFee IIIII III NFe III i III II FFe I e II NFe IIII Fei II III I Fe Fe I Fe IIII III I

1490 1505

1525

1506

1526

1507

1527

1508

1528

1509

0.6×10-9

0.4×10-9

10

5

-5 0

-10

1529 1530


0.8×10-9

χ


F ZNne II TSiii IIIIII III III N iI I FFe I e III I F I Fee II Fe II Fe I I NFe IIIII iI F IIII CFee I I FreIIIIIII FFe III e III I TFFNSeeii I FeiIIIIIII Si IIII FC I NFeo III ieI III IIII N Fei I IIII I

F Ne II iI I I Fe I Fe II Fe III III TFei C IIVI TFei II Fe IIIIII II I

S ZNni II Fei I IIIIIII I Fe Fe III SSi I NFi IIIIII N Feeii IIII IIIII I S SSiii III N I Fei IIIII I N II TFi i IIII e III III Fe Fe III II I

N Fei II II ZTFni II e IIIII IIII TTi ZFnei IIIIII IIII Fe II II I

FFFee FFee III II Fe IIIII Fee IIIII II IV FF Nee III i I II Fe II F II FFNee I I e IIIII II FSei III V FFee III N IIIII iI I Fe I F I e III N II iI TFie II I Si IIII Fe II FFe I I e III NFe IIIII i FFFe IIIII Fee I I Ne IIIV i I IIIII II

C NF II NFei IIIII ei FeIIII II N F ZFnei I Ne IIII Fei IIII II Fe II F II Fe I Tei IIIII Fe II I Fe I I III Fe II FNe I I Fe III NI II

XCIX

χ

1.8×10-9

1.6×10-9

1.4×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

10

5

-5 0

-10

1510

1.4×10-9

1.2×10-9

1×10-9


FFSe FeeIII Fe IIIII I FCe II FFeIII Fee IVI FFFee IIIIIII eI I Fe IIIIIII e III II FFe I FFeee IIIII FFe IIII I ZFnee IIIIII NFe III iI I V I CFF I Ceeu I III ZFFneo IIIV I Zne III Fe IIII FFe IVII e II Fe V II FCFeo III e IIIII II FNei I Fe I I I Fe III F I NFFFeee IIII ei I FFe IIIIIII Fee IIVI Fe IIII I F II NFFe I I eieIIIII F IIII FFee III NFFFeee IIV III NFei IIIIII Feei II Fe IIII Fe IIII Fe IIII Fe III C III Feo III Fe I FCe IV Feo III Fe IIV IIIII Fe I II I FFe FFNeei III FFee IIIIIIII e I II Fe IIII Fe III FFe I I FF e IIVI eI IIII Fe I Fe II Fe I I F III FNFCeee IIII Fei IIIIVII III ZFNCn II Cei II o IIIIII F III FFee II FCee IIV I C IIII F M Men IIIIV Fen IIII IIIIIII M I n II N I ZFFSneii I M I en IIIII Fe IIIV III FSei I II IV CFe IIII Foe III III NFN IV eiiIIIII NFNei IIII FSiei IIVI I Fe IIIII Si I Fe IIII II Fe IV Fe III Fe II M nI I Fe IIII I Fe II II F Me I n II I FNei III FFe III I M Fee IIV FenI I IVI I V FFe Fee I II NNi IIIII i III II FCo Me III n II FFe III e II MFe II M Fenn I I N IIIV i IIII FFFee IIII e IIIV II Fe II MFF III Feen MNFei IIIIV I nI IIII Fee IIIIIIII III

χ


1.4×10-9

1.2×10-9

1530

1550 1531

1551 1532

1552 1533

1553 1534

1554 1535

1555 1536

1556

1537

1557

1538

1558

1539

1559

1540 λ [Å]

1560 λ [Å]

1541

1561

1542

1562

1543

1563

1544

1564

1545

1565

1546

1566

1547

1567

1548

1568

1549

1569

F FFee II Fee IIVI F NFFFeee IIIIII Feei IIIIII FFee IIIIIII I NNi IIIIII i I Fe III FFee III Fe IIIIII F IV Fe C e III r I FFee IIII II FFSei IIV Fee IIIII I I FFe II V Fee IIV II Fe III Fe I Fe III FNe IIII iI I VI Fe I FFe II eI I Fe IIIII Fe III II FSe I I III N I Fei I Fe III F NFFFee IIIIII II FNeeeii IIIIV II FN IIIIIII C ei IIII r I II I FFe I eI Si IIIII Fe III S I FFeieIIIII I Fe IIII IV I Fe I Fe III FSe I Fei III Fe III IIII I NFe I C i I II r I I A II l II FFe I e III Fe III Fe I IIII NFS I VFFei II eII MNFFeei IIIIIIIII Fn IIIIIII NFe IIII FSCeei IIIII FFe IIIII CFeee IIIIII u FFCe IIIIIIIII e IIIV III Fe III F Fee IIIII FFe I I Fee IIV I Fe IIIIII I CF II ue CFFe III Fre IIII CFFee IIIIIII FFoee IIII Fee IIIIIIIII IIIII I Fe F II FFNee I I C ei I I r IIIII IIII FFe I e II III I VFNe FeIi IIIII FFe I I e IIIII Fe III Fe IV I FFe II Fe I NFe IIIIIII ie I I IIII FFe I NFFee IIIII Fei I I FCFeee IIIIIII I Feo IIIIIII FCe I IIVII Fe II I FF II CFeee III Fue IIIIIII CFe III Fue II I S I Fe IIIIIIII II I CF oe IIVII

FFFee Fe IIII II MFFFee IIV V II FFeeen IIV e IIIIIIIIIII III

APPENDIX

χ

1.6×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

10

5

-5 0

-10

1550

1.6×10-9

1.4×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

10

5

-5 0

-10

1570

C

χ

Flux [erg s−1 cm−2 Å−1 ] 1.4×10-9

1590 1592 1572 1573

1594 1574

1596 1575

1598

1576 1577

1600

1578

1602

1579 1580 λ [Å]

1604 1606

1582

1608

1583

1610

1584 1585

1612

1586

1614

1587 1588

1616

1589

0.8×10-9

0.6×10-9

0.4×10-9

10

5

-5 0

-10

1618 1620


λ [Å]

1581

CF Fuee N IIIIVII Fei II NI i III MFe I Nn IIV Fei I II III Fe II N II FNieII i II N I M ZNFni I ieIIII IIIIII

1571

C M r NFenIII Fi I CCFre IIIIII u NFee IIIIIII i I Sc III N i III ZFCneo III III III NFFe I Aei IIIII l I III II CFFFe NNuee III iiI II AF IIII ZFneel IIIV I N NF i IIIIII MFeeei IIIIII n IIIIIII NFe III Fi I I MFFee III II Mne IIV NFn II ie FFe IIIIIIII SFNCceeii III CN M FuenIIIIIIII II CNi IIIVIIII Fo II Ne IIII i IV II NF ieI Fe IIII Fe IV MFe II M MAFNennIIII CNFFCeniliIIIIIIIIIII u II NFeeoIIIIIV i I IIII I C I u NF III FFeei I e I C IIIIIII NFFuee II iI MFNe IIIIII ni II II FFN MNFFNeeeii IIIIII eni IIIIIII I M MFFeen III Fen IIIV III II C IIV I CCu II FFure II FNee IIIVI Sci IIVI F IV I CNFee IIIVIII M uni FFNeiIIIVII CNe IIIVII ri I Fe IIIII AFFe III A ll III NFeIIIIII i N IIIII i NFFe II NFieeIIIII Ni IIIII F i II Me I I Nn II NFFiei IIII CN M reni IIIIIII IIVI Fe II II I Fe N I N NFeii IVI i IIIV III

1570

Fe FFe I F e IIII NFFFeee IIIIII NFei I III i I Ce IIIIII Feo III II I

M FCeo nII III N i Fe II III Fe I NFSei III Fei III IVI NNi IIII Fei IIII III I NF CFNeiiIII Fuee IIIIII IIII I

χ


Fe FFe I e IIII II FFFee e CS IIIIIII r Ni I I i III NNi II iI S III Ni II I i FFee IIII Fe IIIII III I

II MF Feen III Fe IIIII M nIII III

Ti I

II Fe F C e II r II I IIII FFee N IIVI Fei II II MFFFeee n IIIII III Fe III II

Fe I

NF Feei II FNe I I i IIIII II

FFe Fee IIIII C III o I C II F CFNeoi FreeIIIIIIIIII IIII Fe I Fe III MF I II Feen IIV I N IVIII iI I I F F e e C II Fre IIIII I N IV I iII I CFe NFue II i IIII III F NFee II FFei II I CFee IIIIII M r I III n F II CFFeee IIIII FFree IIIIIIII F IIII FFFeee IIII FFNeee IIIIIIII ZFnei IIIIIIIIII Fe III IIII ZFn M FeenIIIII Fe IIII Fe III II I

CFFee CFr IIIIII FreeIII IIIIII I FN NFCeeoi III FNFei IIIIIIIII I FFeie IIV FeIIIIIIIII F FFeee IIIII I FFeee IIV IIII M Fe IV I M nnIIV III I

CF Fuee N IIIV NFei IIII III Fei IIV III I C Fr FeeIIII II F V Ce I o II Fe III F I MFe IIII en I I III Fe II CI FFeo III FCeeo IIIII Fe IIIIII III I

CI

1.6×10-9

1.4×10-9

1.2×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

10

5

-5 0

-10

1590

1.2×10-9

1×10-9


1620 1622

1656

1624

1658

1626

1660

1628

1662

1630

1664

1632

14×10-10

1666 1668

M Fn CFFFee III reeIIIIII IIIII C IIIV Fue I IIII FA I MFFeel I Feen III IIV IIIIII I C u I NF II ei I II M ZFne I F Ce IV o I CNFFee IIIII C Croi IIIIIIII Nr IIIII F i IIII CCFFreee III FueIIIIIIII IIII MFFee I C n IIIIIIII rI I NFFFee II FFeei IIIII Fee IIII IIIII C II r C III u I CNFFei II FoeeIIIII CFe III r II I IIII C u FFFe I Cee IIIII o CF IIIIIII re I I II N iI I CF I No CFFeieIIIIII ue II II NFe I I i CNF IIIII CFreei III u III II I CNFie I NFCroI I i I CFeeIIIIII r II I I CFe II u I N II iI II NFe CNi II ui III NFFFeIII FeieeIIIII Cr IIVIII uI F IIII Fe I NFee IIII C i IV NFr II CZnieIIIIIII u I CFe III u II C III r CFF III oee IIIII I

FFee I Fe IIII II NF Mei MFCnIIIVI Fen I CFFee IIIIIIII I Coee IIV FC IIIIIII CFCe III o FCe IIII C IIVI CFFFee II Fuee III Fe IIIIII Fe III N NFi II M CFenieIIIIII o IIII Fe IIIIIII IV CTF FCSueieiIII C o IIII No IIII NF i I II ei IIIII NFF III FeeieII IIVII CFe V FreI I CF I I NFoe I CFieeIIIIVIII r III N III i F I CFSe I I r I Cei IIIII o II FN I Vei IIIII I N IIII iI II NFe Ni I F i III C e IIII r MFe IIII M CFnne IIII C o IIII rI I II

χ

Flux [erg s−1 cm−2 Å−1 ] 1.2×10-9

1634 1636

1670

1638 λ [Å]

1674

1642

1676

1644

1678

1646

1680

1648

1682

1650

1684

1652

1686 1688

CII

1672 λ [Å]

1640

FFe e CF IIIII NCue FioeIIIIII M III FFen I I Ne IIIIIII i MFe III Nn II iI FFee IIIIII CNFei IIIII Z r CNn IIII NFrieIIIIII i II N IIIII Fi Ce IIII FFoee IIII Fe II I II NF IIII i FFee IIIII e I MFFe IIV II Mne IIIII n II I MFe II n II III I C o F CFe II r N eIIIIII i II V III FNeIi II Fe IIII MF III Men III CFFn IIII Zree I CCFne IIIIVIII u I N TFOoei IIIII C CNri iIIIIIIII CNr IIIII Fo II N NFFeeii IIIIIII Nei IVI MFFFeieIIIIIIIII FFeen IIV Fee IIIIIIIII FFFee IIIIIIIII I CFFeee IIIIII FFuee IIIIIIII II II II

C II MNi I FFenIII NFee III Fei IIIV IIII I II NF V N NFiieeIIII i IIIII III Zn I FSSNei i III FFeieIIIIIIII II NFF IIII MFeeie IIIV I n NFe IIII iI I FFee II FNei IIIIII IVII FAN FFNeeeli IIII CNFei IIIIIIII CFui IIII Fuee I IIII MFFe VII F FFNeene IIIIV ei IIIII NF IIIII CFeei III CFu IIIIII FNuee IIII i IIIII II M ZNFFni I FFFNeee II Feei IIIIIIIII I F IIIIIII NFFeee III i I III N II Mi I FFNen IIII e I N Nii IIIV IIII NFFieIIIIII ei III NFNe IIIII ii I CFFFFCee IVI rI FCeeeIIIIIV I IIIIII I F Me FF I CFene IIIII Fre III FeeIIIIIIII III Fe I CFFe III NFre III ei IIIII II FFee I IIII FSei I I Fe II NI i II I N iI II CFNe u ZFCneoi IIIII FFee I F II Fee IIIVIIII NF I I FFeei I II e IIIVI N IVI CFieII r II I III

APPENDIX

χ

1.4×10-9

1×10-9

0.8×10-9

0.6×10-9

0.4×10-9

10

5

-5 0

-10

1654

12×10-10

10×10-10

8×10-10

6×10-10

4×10-10

2×10-10

10

5

-5 0

-10 1690

χ Flux [erg s−1 cm−2 Å−1 ]

1720 1692

1722 1694

1724 1696

1726 1698

1728 1700

1730 1732

1702

1734

1704

1736

1706

1738 λ [Å]

1708

1740

1710

1742

1712

1744 1746

1714

1748

1716

1750

1718

12×10-10

4×10-10

2×10-10

10

5

-5 0

-10

1752 1754


6×10-10 NNi i III II

C CFo I CFCreeIIIII NFFFreeIIIIII ei I I CNAC No IIIIIII iliIIIIIII C IIII I CN I CNFCrii II SueIIIII NFFei IIIVIIII ei I V II Fe Fe I N CF i I II o II I CNei IIV NFr IIIIII F CFeieIIIIII FAueel IIIIII III F III Fee II Fe I I F I CFFee IV oe IIIII M FFFeenIIIIII e IIIII FFee IIII I S IIII NFei IIV Fei IIII CF I I ue II NFe IIIIII NFFi I FeieIII Ne IIIIIIII Ni I I I i III II N iI N C i III Foe III FFe IIII e I FFee IIII NFFe IIIII ieIII IIIII CNFFe Moei III n III N III iI I CM Non I NF i IIIIIII i I TFei IIIII M enII I M FNe IIII g CC i IIIII FFro I N Neie IIIIIIII Ni IIIIIII CFei III o III III I Fe I M I g M F II NNeni IIIII M FNeinIII CNFeii IIIIIIIII o F IIIIIIII C e II u CNF i III oe I I M FenIIIIIIII II NFF III Nei CFeei IIIIIIII CFu IIIIIII M MNueni IIII NF n IIIIIII M einI Fe IIII I FFFNee II e III M IIIII n I N I iI Fe II II I Fe FNe III M CCFoen II r II FFe IIIIIII eI Fe IIIII NFFFNeee IIII ii NFFe IIIIII i Ne IIIIIIII Ni I I FNe IIIII FFei III e II II I FFe III Ne III Fei I II ZFNn IIII e I Fe IIIIIIIII CFFFee IIII u III M IIII g I Fe II Fe II I NN II NNCi III I NiiIIIIII FNei III i IIII II N I Ni I I i NM Fei IIII gIIIII I

1690


CN ri I II CNFi IIII NFreIIIII i I II e Fe IIII I F I CFee III Fre I III I N IIII i NI CFFeieIIII Cu IIIIIIII r I Fe III NFe III i III I FFFeee I N IIIIIIII Fi NFFeeIIII i II FFeeIIIIIII FFee IIIII e I NFe IIIIII i II CNi IIII No III i II F II I C e II FFFre I I ee III IIIIII FFe e CC IIIII r I NFFoeeIIIII NFi IIIII ieI I IIII NFFNeei iI NFeeIIIIIIIVIII i Fe IIIII II I C NFr I i C e IIIIVII u I N II Ci I CNFFre IIII FreieIIII C IIII C CFFCueeI I u III II N III CFi I C roe III u IIIII F IIII NNei III i I F IIII Ne I I Ni III iI I F II NFe I ie I FSe IIIIII i C III u C II u I CFe III Nr II Ni IIIIII Fei I I ZFne IIIII I FNe IIIII i II CN N Noii I III C CFri IIIIII r II C eIIIIIIII o M III NFF n II eieI C Cu IIIIIII Fure IIII FFe IIIII NFNei IIIII NFei I II Fei IIIIVI F II CFee III Fre IIIII FSei IIIII CCFre IIIIII CFFSuei IIIIII CFFuee IIIIII r II N M NFeienIIIVII i II II III N Fei II FNe I I FFei IIVI eI N IIIIIII N i II Fei I CNi IIIIII r I NFe IIII M in NFFe I III FeieIIIIII Fe IIII N III iI I I F I Ne I i I CFo IIII r MFFee IIIII ne NF IIIII FeieIIIII I F C e III Fre III F II FFee IIIII MNFFFe I I eenie IIIV CNFei IIIIIVIIIII r IIII III N NFFeieI I i I FNAe IIIIII ilIIII III CNFei I r III III

CIII

12×10-10

10×10-10

8×10-10

6×10-10

4×10-10

2×10-10

10

5

-5 0

-10

λ [Å]

1720

10×10-10

8×10-10


1790 1792 1794

12×10-10

11×10-10

1796 1798 1800 II

1802

1772 λ [Å]

1804

Flux [erg s−1 cm−2 Å−1 ] 8×10-10

1806

1776

1808

1778

1810

1780 1782

1812

1784

1814

1786

1816

1788

1818

CIV

λ [Å]

1774

N NFieI i IIII I Fe II II I N MFei II Mn IIIII I CTFin III CNoe II I N NFFoeii IIIIII i I NFFFCNeee IIIIIIIII NSeioiIIIIIII i III CN IIIIII NFFoei II N F e C i IIII CFoei IIIIIIII Foee IIII IIII FFe II FFee IIIII Ce I I o IIII II C II o II FFe I N NFei IIII I i e I C CFoe IIIIIIII o FFFFeee IIIIII e I I Fe IIIIII I Fe III II NFSei I I Fei IIIIII I NFNSni IIII CM FoeeiiIIIIII I I Fe IIII II I CFe o II II I CN Noi Fei III FFFe IIII e CFFee IIIII re IIIII IIIII I

1770

MN Nni i IIII II Fe III N N Nii IIII i IIIII C III Fo FSee IIIII Fi Ce IIII o II II I

1768

FFe CSe IIII o II II I

1766

N i Fe III II I CNF i re III F III TSeii IIIIII N Fe IIIIII II I S M II n NN III iiI II

1764

II

1762

iI

1760

N

1758

N iI

1756

M MTn I FeinIIIIII IIII I MTFei I C n II M Fo I NFFenee IIIIIIII i I II II N iI II

C No I i I II II NF ei I C CFo IIII o I Ne IIIIII N ii I III IIII CFe I o CN IIIII TTFoii III ei III I N IIIIIIIII N ii I FeIIIII CNF II Crei MFoe IIIII n III III I C No i III N III iI II

χ 10×10-10

A C l II r N III iI II C o C I o II ZAn III N lI C i IIII Co I I o I C IIII u C II rI I NF II C ieIIII NFo I I ei I II TFei IIIII Fe IIIII F Ce IIII NFo IIIII CFeei IIIIII FFFoe IIII ee IIIII FFe IIIIII Fee IIIII F CFee IIII o CFFe IIIIIIII NFoe IIIIII Nei IIIIII iI C IIII No II iI I I Fe I FFe I Ne IIIIIII i NFFee IIII FFei IIIII e IIII NFFee III CNFei IIIIIII oi II IIII TFi III e F C eIIIIII o II II N TSii I N Fei IIIII MN I I I NF ni IIII FFeei IIII ee III C F C o III r I Fe IIIII Fe II N IIII NFi I ieIII IIII Ti Fe III N II CF i I I SSoei II Ni IIIIIIII Ti i III CC III ro I TFFi IIIII eI NFe IIIIIII ei I FeIIIIII Fe II C II o CSFe III Soii I F IIIIIII CNie III oI Ti IIIII N SiI I NF III NFFeeieIIII i I NN IIIII FeiiII I CTFFFei IIIIII oee I I FFe IIIIIII eI N F Nie IIIII i IIII IIII

iI Fe II C III o II I N Ni I I iI I Ti II II I C NF II ie I II N TSCi IIIIIII Fe I II Ti IIII FeII A II CNFCil II oe I N MCi IIIIIIIIII CnIIII Fe IIII FFe I FFee IIIII II Ae IIIII l I N II Fei I IIII CNFie I r C IIIIIII I o CNANi III FArellIIIIII Fe IIIII F III NFFee III ei III I III

N

APPENDIX

χ 12×10-10

6×10-10

4×10-10

2×10-10

10

5

-5 0

-10 1790

10×10-10

9×10-10

8×10-10

7×10-10

6×10-10

5×10-10

4×10-10

3×10-10 10

5

-5 0

-10

1820


CFFe I NFoee III Ni I III i SAilIIIII II MF II ne I FFe IIIII e II III I FAe M Fenl I III F IIII Ne II iI I Fe II M CN III oni FFFeeIIIII FFee IIIIII e II M IIIII FNen I Fei II I IIIII I Fe CM n o II III I FAel I CM AonIIIII l IIII N III i CFe III o II C CFo IIII o Ce IIIIII M FFoe IIIII FenI I FFFeeee IIIIII Fe IIIIIIIII CF I FFoee II Fee IIIIII M II NFFenIIIIII ei Fe IIIII Fe IIII FFe I I Ce IIIIII No I I i I II II N i Fe III Si I MFFe IIII CSeni IIIII Fo IIII F e IIII I FFeee II II Si IIIIII Fe III Si II Fe III FFe I Fee IIIII C Co IIIIII FFoe IIIII CFee IIIIII Foe I I Fe IIII F FFee IIII Fee IIIIIII III CF I oe I C II CFoe II o Fe IIIII II I I FFee IIII Fe I II C F C MFooee nI TFi IIIIIII e III I II FFee I I TNi IIII C i IIII Co I I o II III I Fe II NF I Feei II F IIII FNe III Cei IIII F Coe IIII Co IIIII Fo III CFe IIIII oe I N III FFei I I CFFee IIIIII oe I I IIII I Fe III Fe III I NFFe III Fei I MFee IIIIIIII n IIII III NF I FNeei II i IIIIIII C II FFoe I e II FFFe IIIIII e Fee IIIIIIII Fe III III CFFee I I o FFe IIIIIIII e III I C I Foe I Fe IIII III I

1820 1822

1856 1824

1858 1826

1860 1828

1862 1830

1864 1832

1866

1834

1868

1836

1870

1838 λ [Å]

1872 λ [Å]

1840

1874

1842

1876

1844

1878

1846

1880

1848

1882

1850

1884

1852

2×10-10

10

5

-5 0

-10 1886 1888 1890


4×10-10


CF oe FFee III I FN IIII CFeei IIII oI I II C CFFoe III CFoe III CFFFoeeee IIIIIII r I Fe IIIIIIIII NFei III CN oi III III M CF n III FNFFFoee IIII e e FSieeIIIIIIIII IIIII Fe I C I N No III CFFeii IIIIIII oe III III M Cn I o FFee IIIII FFe IIII e IIIIII II CFe I C o III Cr I I I FreIIII II NF I MNieIIII FFeni III Fee IIIIIIIII II C CNo I r CN Noii IIIIIII F i IIIII CFFee IIII o I NFFFee IIIIII eieIII I F CF e IIIII NFoe III F C ieeIIIIII CTFNoe IIIIII oi II NFFNieIIIIIIII eii MF IIIIIIII FFFeeene II IIII CNF IIIIIIII oieI I Fe III N II iI I CNF II CFFoei CFoeeIIIIII NFoe II CCoieIIIIIIIIII Fr IIII CTieIIIIII Foe III II N III C i II rI I F CFee III CFFoe III oe III II Fe III FFe III e N Ti III I III FCeo I I Si III FeIIII I FFe II NFe IIII Nei II I i I CFe IIIII u I I FFe II FFee I e IIIIIIII Si I F II Sie III FNe III i F IIII C CNFFoeeie I I No IIII i I Fe IIIII Fe I I Fe IIII I CFFee II Foe IIIIIII Fe I I Fe IIII II C MFo II CFen IIII FFoee IIIIIIII FNe I II MNFei IIIIIIII i I FFeenIIIII CM FFoeeenIIIIII Fe IIIIIIII FFe IIIII I NFFe IIIII C MFreieIII I CNFenIIIIIII CNoei IIIII Foei IIIIII TFei IIIIII Fe II II FFee II M Fe IIIII nI I NFe II FieIIIII C III o Fe III F Fee IIII F CNe I I oi III M C IIIII N on I iI FFeeIIIIII N IIII CF i I I oe I CAF l IIII Foee IIII IIIII I

CV

10×10-10

8×10-10

6×10-10

4×10-10

2×10-10

10

5

-5 0

-10

1854

10×10-10

8×10-10

6×10-10


M FFen e IIIII IIII NFe I FFei I II M Fee III FenIIIIIII FFe III e III III Fe Fe II M nI I M N n IIII i I Fe IIII F I Me IIII Fn I Ne IIII i I II Fe II Fe I M I TFeinIIII FFeeII FFe IIIII I M FeenIIIII Fe IIIII FFCe IIII FFe II I Cee IIIIIIII FFoe I II FFee IIIII FC I C CFFoeee IIIIIII CFoe IIIII FFoee IIIII Fe IIIIIII TFFeeie IIIII CFe IIIII Foe IIIII F I II CNFeei IIII oI I FACe I II FFel IIII M FeenIIIII Fe IIIII IIII Fe II FFe II e I Fe IIIII C III o F MNe I ni IIIII IIIII I Fe I C II CFoe II oI TFie IIIIII III A Al N Nil IIII FFei III MFee IIIII n II CFFe IIII MFFoee IIIIIIIII nI FFNeee IIIIIIIII C i IIIII o II Fe IIIII II I FNei Fe III Fe IIII NF I I Nei I II i III CFe II M Mon IIIIII FFen III Fee III IIIIII MC III CN TFoino I CSei IIIII oi II Fe IIIIIIIIII C Co I I o II CN M Noi IIIII MFni IIIIIIII FFeen IIIIII e I III I TFei III TNi III MCi IIII nu III C II Foe I Fe IIIII II Fe I CNF III Foei I Me IIIIIII Mn I n II Fe IIII MFFe II Fen I I CTFeie IIIIIIII TFoei IIIIIIII Fe III M IIII Fen II M CFFSenei IIIIII o I C IIIIIII M Feon I I T IIIII I C CFoi III o Fe III Me I III n II II CF I MFoe I MN NFFeenni IIIIII ei IIIIIIII IIII NFFe I FNeeiiIII III CFFFe IIIII FFoee IIIIII e IIIII II CCFFooe I re III IIIII I


1890

1920 1892

1922 1894

1924 1896

1926 1898

1928 1930

1900

1932

1902

1934 1936

1904 1906

8×10-10

7×10-10

1940

1910

1942 1944

1912

1946

1914

1948

1916

1950

1918

1952

CVI

1938 λ [Å]

1908

MF en II II Fe II F II NFFee III FFeei IIIIII Fee III IIII II M F I NenIIII M FFei I I enIII N NFCi IIII ei III NFe IIII CCi IIIII o II I I Fe II II I Fe FFFFeee IIII I e Fe IIIIIIII Fe IIII F FNee IIII Fei I I Fe IIII M nIIIII CFe III Foe IIIII Fe III M nIIII II

F Ce I o II II FFe I e III II FTe I i FFe IIIII e Fe IIIIII I Fe II MFFee III n III III FTei III I FCe IIII M IIII N n II i I Fe IIII TI FFeei III II FCe IIII Fe II FC I I CFeeI III o III II FFe I M FFFeenIIIIII ee III IIII I

N i Fe III Fe I FFe IIII FFee III Fee IIIIIIII Fe III I MF IIII CFSen FFoeei IIIII FFee IIIIIIIII FFee IIIIII FFee IIIIIII II Fee IIIIII III I N i FFe II Fee I Fe IIIIIII Fe III II Fe I CNF III FFoeei I FFee IIIII Fee IIIIIIIIII NII Fei III III FFee I Fe IIIII I FTe III Ni III i III I F Me II n I Fe II I Fe II MN II Feni II I IIIIII F I Fee I IIII I Fe NN III i F iI CTFe IIII Foeei IIII IIII FFee I F IIIII Ne II i Fe IIII M NFFenIIIII ei IIII II Fe III Fe II I FFe III Fee I IIIII III

9×10-10

APPENDIX

χ 10×10-10

6×10-10

5×10-10

4×10-10

3×10-10

2×10-10

10

5

-5 0

-10

λ [Å]

1920

9×10-10

8×10-10

7×10-10

6×10-10

5×10-10

4×10-10

3×10-10

2×10-10

10

5

-5 0

-10

1954


1990 1958

1995 1960 1962

2000 1964

8×10-10

2005

1966

F SFFee I TFFceeieIIII M C MFrnIIIIIIII M CFFCeenoIIIII Foen III CFFee IIIIIIIIIIIIIII M FreenIIIIIII IIII MFe III CFne II ro IIIIII I CFFe I I M FFSreeni IIIII II I e FFee IIIIIIIII I MFe IIII FSeni III I FFee IIII Fe III I MFCeIIIIII MFCn II FeneIIIIII N IIIII i II M I n I F II M MNnei I M n Mn IIIII MFCen IIIIIII no II I IIII MF II en I Fe IIIII II M Mn I Mn I MCFFen IIIIII eu I FFCeno IIIIIIII e IIIIII IIII M M MNCnno I ni IIII M I F I M MNFnnie IIIIII CenIIIIIIIIIII o IIII II Nei II MFFN eni IIII IIII M Cn Cr M MrnIIIIIII M n II M CFen IIIII on I M MFFNne IIIIIIII nei IIII MF IIIIII en I F N M MFeni IIIIIII en IIII MFFe IIIIIIII CFeen IIII M FrenIIIIIIII MFNe IIIIIIII CFni IIIIIII u CCFe IIIIII M FroeI I CM CFFren IIIIIII M FeeenunIIIIIIIII M F nIIIIII MFe III MNFFeeeni IIII nIIIIII CFe IIIIIII M MrnIII II MFFFen IIIIII Feene III I I F IIIIII C e III r Fe IIII MNF III en FFei IIII CFFe IIIIIIII ue II Fee IIII IIIII

MNFAilI en II MFFe IIIIIIII Fene III II FFee IIIII M C CFFren IIIII M r MNFenIIIIIIIIIIII Ceni IIIIIIII o II M FFFee IIIII enI Fe IIIIIIII CFe III F o MNe IIIII ni III Fe IIIIII M Mn III n II III MF I en II MFe IIII Fen I C CCFFFFFreee IIIIIIII FreeueIIIII IIIIII FFe II e MFFee IIIIII I CFFen IIIIII Fre I CFee IIIIIIII Mr IIII FFen III Fee IIIIIIII F III CFe I I FNreeIIIII i II FFe IIIII Fe I Fee IIIIII III MFe II n III Fe III F I FFeee II II Fe IIII II I

1956 1968

2010

1970 1972 λ [Å]

2015 2020

1976 1978

2025

1980

2030

1982 1984

2035

1986 1988

5×10-10

4×10-10

3×10-10

2×10-10

10

5

-5 0

-10

2040 2045


λ [Å]

1974


M n N III i CNi III oI IIII M I MFne I n NF IIIII Feei I II IIII M C n IIII Fre IIII C I II M o Fen IIIIIII Fe I I I N IIII iI I Fe I F I MFe IIII en II I Fe IIII F MFe III Cen I CCNoui IIIIIIIII Fre IIII IIIII N I iI C II No I i I II II MFe n II N II MF i I II en I Fe IIIIIII FFe III eI Fe IIIII Fe II FFe I I Fee IIIIIII F III Me III n I M II n I CFe III Fre I MFe IIII Fen I II C IIIII CFe II I FFCre IIII I Ce IIIIIIII II I FCe III II F M CFee III n o CF IIIII eu II I III

CFe CTFFoe III Toei I III Ni IIIIIII MFei I IIII CNn IIIII Frei IIIIII MFCeo IIIII Fen IIIIIII Fe IIII M IIII FFen I Ae I II FFel IIIIIII M CFFeenIIIII o Fee IIIIIIIIIII I Fe III Fe I IIII I FFe NFe IIII ie I II F IIII Me III Fen I I IIII MTFFe I I CFeeinIIII r IIII MFe III M CNn II Foeni IIIIIIII FFFee IIIIII e II NF i IIIIII CAelIIIII r F IIII CNei III r IIIII I FFe I Fee I IIIIII F I Me II I Fen II I FFe III Fe II N e IIIII Fi I I MFee IIII n III II I MFe MFen III CTn IIIIII Foei IIIIII IIIII FFee I I I M III Fen II I I C II o MF II Fen I Fee IIIIIII M III n II II I

CVII

χ 9×10-10

8×10-10

7×10-10

6×10-10

5×10-10

4×10-10

3×10-10

2×10-10

10

5

-5 0

-10 1990

7×10-10

6×10-10


2090 2048 2050

2095 2052 2054

2100 2056 2058

2105

2060 2062

2110

2064 2066

Fe F II C e III Cr I CFr III M CFFreeneIIIIIII FreIIIIIIIII M III n CFe III Fre IIIII M IIII Cn r III CFFNe III CCreiI M C MNrrnuIIIIIIII CFniIIIIII re IIII Fe III C II MFFFNree II I C nei IIIIIIII r I MCNuiII I I C n IIIIII MNriI I n II FNe II Fei III I I N III i CNi II r Fe IIII II MFFe II Fene III N Ni IIIIII i II C I C CFrre II r IIII III F CNei II CFNreIIII r III FeiIIII FFNei III I Ce IIIIII FFSeu I I I CFSeii IIII FCree III I I I CFC I NreI Ni IIII i C II Fre II III I MFe I CFne III r I M C IIIIII CNrnII r CFeiIIIII FNre III I Fe III FF I CFee IIIIII M renI III IIII I

2046

N C iI C FFNrreiIIII e IIIIII III CC NFreu i IIIII C II Mr III Fn I C e IIIII CFr I I r I CFFeeeIIIIII M r FFNeneiIIIIIIIIII MF IIII MFNen IIIII C nei IIIIII rI I MFFe II Fnee IIIII II I FN CFei III u Fee IIII IIII FN II C CFNreii IIII I CFre IIIIIIIIII Cre I I Cr I I I r III II

M MFFNeni e C n IIIIIIIIIII r Fe II I Fe I I IIII I Fe FN II C ei II I M FArenIIIII MFANeli IIIIIII MFFFAenel III Fenl I II MFee IIIIIIIIIIII n III FNei IIII I FNe IIII TFFi i I MFFFeeeeeIIIIIII n IIIIII III FFe II FFeee IIII I CTFe IIIIII M ri I I CNniIIIII Cr I I MFre IIIII n IIII III I

χ Flux [erg s−1 cm−2 Å−1 ] 7×10-10

6×10-10

2068 λ [Å]

2115 2120

2072 2074

2125

2076 2078

2130

2080 2082

2135

2084 2086

2140

2088

2145

CVIII

λ [Å]

2070

MFF en MFee IIIIIII I Nn IIIIII i FFe IIII Fee I IIIII II Fe I CFe III r III Fe III II F M e II MF n I Men IIII n IIII II I F Fee II I II Fe Fe I Fe III M Mn IIIII n II III FNei I I III I FFNei e IIIII M C C nu III Fr I MF eIIIIIII Feen I NFe IIIIIIII iI MFe IIIII Fen III MNi IIIII NFNn IIII i FSeeiiIIIIIII FSe III CiI I MFSeo IIIII ni I I Fe IIIII II I CF M renI IIII I MF MFeen II FFen IIIII e IIIIII IIII MF M Menn III n I MCFe IIIIIII no III II I Fe Fe I C III M o III Fn I MNNe III nii II IIII II MFe n II I F II Fee III Fe II CFe III M rnII I IIII I MF ne FFee III I Fe IIII N II iII Fe I Si I II MS I ni I M II Fen II I FFNeei III IIII I Fe C C Crr II MFreIIIIIIII M Fenn IIIII III I CF II Mre I I Fn I I MFFee IIII n C e III r II FFFNeeiIIIII eI MFe IIIIIIIIII n II III FFe I e II III M MNni I n III III C I r Fe II Fe IIII I MF II Nen II i IIII MF II Feen I FFNe IIIIIII ei III I IIIII Fe FFee III M IIIII MF n I I en II FNe IIIIII CFei IIIII r II I MFe II FNeni IIII IIIIII I

APPENDIX

8×10-10

5×10-10

4×10-10

3×10-10

2×10-10

10

5

-5 0

-10 2090

8×10-10

7×10-10

6×10-10

5×10-10

4×10-10

3×10-10

2×10-10

10

5

-5 0

-10

2190


2150

7×10-10

2195 2152 2154

2200 2156 2158

2205

2160 2162

2210

2164 2166 2168 λ [Å]

2215 2220

2172 2174

2225

2176 2178

2230

2180 2182

2235

2184 2186

2240

2188

4.5×10-10

4×10-10

3.5×10-10

2.5×10-10 3×10-10

10

5

-5 0

-10

2245


λ [Å]

2170

I VFNe Ii N Ni IIIII CNi IIII ui Fe II M C n III r II IIII

2148

Fe I


CF re I I CFN Neu I ii III I N III FNei II i III II CFe Cr I I M FrenI I IIIII C Cr I r II N IIII i CF II FFreeI e N IIIIIII Ni IIII M CFNnii III M FreenIIII FFNeei IIIIIIIII IIIIII III M n FFee I I Fe IIIIII M CFFene II Nr III iIIIII I FFNeei I IIIII I

Fe II Fe MC CnII I FN iIII FNeei IIIII N IIII Fei III N II iI I CFe M r FNneIIIII I i N IIII iI I

Fe N II FFei III eI FF IIII CFFeee IIIII reII I IIIII C I r CF II CFFreeI I Mre III Fen IIII M IIII C CCrn IIII ruIIIII C I II rI II MFFe n Fee IIII II Fe I II FN I CFeei II rI Fe III C III M rnI CFe IIII r I II II MN Fnei II Fe I I III I CFNi re III Fe IIIII M III Fn FNee III CNi IIIIIII riII I CN III riI III I Fe C II FFFNreeiII I Me IIIII CFNn IIII FreeiIIIIII N I II i III I N iI C I Fre I Fe IIII Fe III I FNe I MNii IIII n III CN III FFreiIIII Fee IIII II FNei IIII N II FFNeei II CNi IIIII riIII I FNei II III N M MNni II ni III II C II CFr II re I I II C rI II

7×10-10

CFFree IIIII I N iI C I r F T MFFeieII enIIII FNei IIIIIII IIII

2146

CN ri CNiIII rI TNi IIII iII I Fe II C CNri CNr III CriIIIIIII r I Fe III I M C n II Nr C iIIIII r III C II r FeIII N II Ni I C i II FNoe III Ni I CNii IIIII r II III CF re I N IIII i Fe III CFN Neu III ii II III F I C CNrei I r I N M iIIIII MNni IIII Nn IIIII N Nii IIIII i Fe III Fe II F FCee II I M o IIIII n I C III CVrII Nr III C iIIIII Fr I V eIIIII C CNrI CCNriIIIIIII ru CV IiIIIIII r III I CFN I ri CFeeIIIIIII oI M MFFNenei IIII n FNei IIIIIIIII II CFe III r FNeiIIIIIII N III iI FN Nei I i III N I i CFFN Nreei IIII SiiIIIII N III iI CNi II Nr I I MFFNeii IIII FFNeneei IIII I M IIIII CFen I Feu IIIII I N IIII iI CNi I r III II CFe Fr I FeeIIIIII F I Ve IIII IIII CFe I FreIII IIIII

CCNui M CFrenIIII r II CNiIIIII r CFNeiIIII Cr IIII r II I CCN i II ANuoi III l II I MFCNe noi II A IIII lI I Fe FAel II FFe IIII e IIIII II

χ

CIX

7.5×10-10

6.5×10-10

5.5×10-10 6×10-10

4.5×10-10

5×10-10

3.5×10-10 4×10-10

2.5×10-10 3×10-10

10

5

-5 0

-10 2190

6.5×10-10

6×10-10

5.5×10-10

5×10-10


2290 II

o II VFFe CeIIIIII Fo II CFee III Cr IIII Fue III III C Fre I N III Ni III CFei II N IIIII Ni I C i III FNreIII Ni I I i II I CNi No III C i II r I N II CF i I I oe I II N FFei I N I FFeei IIIIII Ne IIIIII N ii I I III Fe N II Fei II II Fe II Fe I CN I M oi II Nn I FSeii IIII III CF reI IIII F CNSe I o Feii IIII CNi IIII No III FFei I Ce I MCFo IIIII noe II C II I Cr II o I FNei II N IIII iII I C o Fe I I VF II FFNeeII I CF ei IIII Free III N IIIII i M III Fen IIII FFe FFee IIII FFeee III IIIII II Fe II V III FCNeoIi II CC IIIIII rI I FCeIIII FeII C IIII o CFN Noe I Fei IIIII I F Fee III FFCee III IIIIII F M FFeegI Ne III VCNoi IIIIIIII Ii FFe IIII TFFeie I Tei IIII V II III Fe III CFe III r III II V Ti I N III Fei IIII II I C o FFNei II VNei IIIII F I III CFe IIII Noe I F i IIIII V TFeei III FeIIIII Fe III CFFFe III ree I CFNeIIIIIIII oi II I F I CFee II r III V II FNeIi II I CFFNei II oe I II

C

rI

6×10-10

C

χ Flux [erg s−1 cm−2 Å−1 ] 6×10-10

5.5×10-10

5×10-10

2246 2248 2250

2295 2252 2254

2300 2256 2258

2305

2260 2262

2310

2264 2266 2268 λ [Å]

2315 2320

2272 2274

2325

2276 2278

2330

2280 2282

2335

2284 2286

2340

2288

CX

λ [Å]

2270

C

rI

II

Fe I C I r N III iI I C o C II rI II C o Fe II C II r Fe III II I C o C II rI CN II ri I N IIII iI I

N i C Cr I I Cr II Nr IIIII FNi III CCNuei III rI FNeiiIIII II CNi III r III II N i N II iI I

iI I N i C II rI II

N

N i N II iI I

FNe F CNeii IIIII r II N IIII iI Fe I MCo II Fne I IIIIII FFe C e IIII MFreIII n III Fe III II

F CeI Nr I FFFNeeiIIII Nei IIIIII CCFei IIIIII roIII II C CFre r CNiIIIIII r II I C II rI I N I Fi I CFe III Foe FNee IIIII Fei IIII IIII F Ce r III III CF reI Fe IIII II

C FreII N II i I M II Fne IIIII CFe r CFN IIII r I C eiIIIII FFre II eII N IIII Fei III II N Ni I M gi III II

FFe e II I CNi III o FNe III Fei I IIIIII I CFe u N III C i III rI II

APPENDIX

χ 6.5×10-10

4.5×10-10

4×10-10

3.5×10-10

3×10-10

2.5×10-10

10

5

-5 0

-10 2290

5×10-10

4×10-10

3×10-10

2×10-10

1×10-10

10

5

-5 0

-10

2345


6×10-10

2390 2395 2400 2405 2410

2366 2368 λ [Å]

2415 2420

2372 2374

2425

2376 2378

2430

2380 2382

2435

2384 2386

2440

2388

3.5×10-10

3×10-10

2.5×10-10

2×10-10

1.5×10-10

10

5

-5 0

-10

2445


λ [Å]

2370

II

2364

II

2362

o

2360

o

2358

C

2356

C

2354

F Me II M n Fen IIII FFe II e F II CFFee III FFreeIIII e III FF III Feee III N II i III I CFe Fo I FFeee IIII MFN IIIII nei I N II I iI FFe II CFee IIII r I II II Fe Fe I FFe III MFee I MNn IIIIII Feni I I IIIII I Fe II FFe e III II

2352

Fe CI o II I Fe I Fe II II FFe I II e F M Mne IIII Fne IIIII F II I eI Fe I Fe I III

2350

C FFNeiII Ce III NFeIIIIII iII Fe II CVC II roI I CFeIII o FNe IIII i III N I i NI FNei III I F i III Ce II MFoe II Cn IIII Co III MFo III Fnee II I FFe II e III F I C e II o I N I iI N I CFei III TCFri III oeI I II FFee IIII I C CNo oi III I F Ce o II I C I Foe IIII FFe e III II

2348

Fe Fe II FFe II e II II

N FieII I N II i Ni I I II VFe III I N FN Feeii III FFe III e III I Fe I C I o II

FCFee o II III

2346


C Co I I o N II Fi NNeIIII iiI I FFe II FFee III C M oe IIIII n II II I

F CeI rII I C I Fo I e I VFe II FFeIIIII CFee IIIII o I II Fe N II Fei I III

CFe o FFe IIII FFeee III IIIII

Fe FFe II eI M III MFFFeen II nI Me IIIIIII n II II TFC Ci I I NeIIII i II N I FFeei II Fe II IIIII I

Fe I FNei I I C I u I FFe I Fe I Ve IIII IIII I

CFFe oe II II Fe Fe I N Mi III Nn III NS i IIIII Vii III FNeIi IIII FSe I Si I Ni IIII iI I

C o V II FeIII Fe II FN I FFeei IIIII Ce I Co IIIII o I II Fe Fe II II

N iI Fe I II

II CS o Fei II II MFFee I NFn IIIII ieIII Fe IIIII II

Fe I

Fe NI M i IIII n FFNei IIII e IIII II

C o I N I FN eii I III F Ce TFio III eI I C IIIII o C II o FFFeee III IIIII I

CXI

χ 6×10-10

5.5×10-10

5×10-10

4.5×10-10

4×10-10

3.5×10-10

3×10-10

2.5×10-10

2×10-10

10

5

-5 0

-10 2390

5.5×10-10

5×10-10

4.5×10-10

4×10-10


2490

5×10-10

2495 2500 2505

2462

2510

2464 2466 2468 λ [Å]

2515

Flux [erg s−1 cm−2 Å−1 ] 4.5×10-10

2520

2472 2474

2525

2476 2478

2530

2480 2482

2535

2484 2486

2540

2488

2545

CXII

λ [Å]

2470

Fe I Fe I II Fe II FFe e III Fe I CM rI FFenIIIIII Fee I I FFNee IIIII i IIIII I Ti FFeIII Fee IIII I CSFie I oII III F Me n II F M N e II inII III

2460

CF o FNeei III FFe III Fee II I Fe III Fe I FFe III Tie II III C II o FFee II Fe III CF III oe I C I rI II

2458

Fe Fe II Fe II Fe III FFe II Fee III Fe II Fe III I Fe I II

2456

Fe NI i Fe III II Ti M III Fen I III

2454

CNi I Foe II II FFC CeeIII FeIIIII II

2452

Fe Fe II II Fe I II F Fee I Fe II Si III II Fe II N CCFFNeii III roe I FeIIIII M II n Fe II I FCe I III

2450

Fe Fe II Fe II MFe II n II II

2448

I

2446

Fe I

Fe Fe I III FFe e II Fe II II Fe II FFe e II I Fe I II

χ 5×10-10

I

I

Fe I

I

Fe FFCe II e III FFe I e C IIII r FeIII II Fe Fe II I FFe I Fee IIII C II rI I Fe I FNe II i Fe II II C o II CFe oI III

Fe Fe II II

Fe I

Fe II Fe II Fe I I Fe I FFe I e IIII I FFe e Fe IIIII F II C e II r FNeiIIII III

Fe Fe II I Fe II CFe II o II II Fe Fe II II Fe II FFe e II II

Fe I Fe I FFe II e III I

CFe FreIII IIII

CFFe reII IIIII

M F CFeegIII Foe II II N I FFFeei II e IIIII I M n M II n I Fe I Fe II Fe II II N iI I

Fe CFFe II oI Fee IIIII II F Fee CF IIII oe I I N I iI II

Fe I

APPENDIX

χ 5.5×10-10

4×10-10

3.5×10-10

3×10-10

2.5×10-10

10

5

-5 0

-10 2490

4.5×10-10

4×10-10

3.5×10-10

3×10-10

2.5×10-10

2×10-10

1.5×10-10

10

5

-5 0

-10

Flux [erg s−1 cm−2 Å−1 ] 4.5×10-10

2590 2595 2600 2605 2610 2615 2620

2572 2574

2625

2576 2578

2630

2580 2582

2635

2584 2586

2640

2588

2.5×10-10

2×10-10

1.5×10-10

1×10-10

0.5×10-10

10 0

5

-5 0

-10

2645


λ [Å]

2570

F Me II n II N F i Me II n II C II rI Fe I III Fe II

2568 λ [Å]

I

2566

Fe I

2564

Fe Fe I III Fe FNe II i III Fe I FN Feei III I M II Nn I Fei III II

2562

F MFFee I C enIIIIII r I FNeiIIII II

2560

Fe Fe II II

2558

FFe Fe I Ce IIIII o FNe II i III Fe I C II r Fe III Fe III Fe I M I FenIIII I Fe II II FFe Fee III III Fe II

3×10-10

2.5×10-10

2×10-10

1.5×10-10

1×10-10

0.5×10-10

10

5

-5 0

-10

rI II CFFre FFeeIIIII Fee III N IIII i III I

C

CCo r III Fe II Fe I III MFe n II II

FFe Fee I IIII I

FCFeo Fee IIII I Fe IIII II N i C II rI II

M Tin I I FeIII II Fe II M n Fe II II C Tio IIII I

Fe FC Ce III III I

Fe Fe I III

Ti I N II FFei II Fee III Fe II II Ti I II I Fe Fe II II Fe II Fe Fe II II Fe II

Fe Fe II II T TFiieI M CFenIIIII o II II

Si N II i Fe II II Fe M II n Fe II Fe II II M n I CSFieI I o II I F CFNee II FFoei IIII e IIIIII I

I

Fe I

3.5×10-10

Fe Fe II II CMFFe I FreeI I FFen IIII III FFNee IIIII Feei IIIII Fe II I FFe II e FFe IIII Fee I IIIII

2556

Fe FN MFeei III FenIII N I Fei IIII I Fe II II Fe I Fe II Fe I Fe II F I MNei III nI I Fe I Fe I I N Fei III III

M n II M n II

I

Flux [erg s−1 cm−2 Å−1 ] 4×10-10

2554

2552

N iI

χ 4.5×10-10

2548 2550

Fe M II n FFe II e II II

VFFe FeeIIIIII III I

M Fen I III Fe II Fe V M I II MF nIII enI I III

2546

CXIII

χ 5×10-10

2590

4×10-10

3.5×10-10

3×10-10

χ Flux [erg s−1 cm−2 Å−1 ] 4.5×10-10

-10 2745

2750 2755 2760 2765 2770 2775 2780 2785

II

II

2790 2795 λ [Å] 2800

2700 2705

2805

4×10-10

3.5×10-10

3×10-10

2.5×10-10

2×10-10

1.5×10-10

1×10-10

0.5×10-10

10 0

5

0

-5

2810 2815 2820 2825 2830

2735

2835

FFe e III I N iI I Fe II

2730

Fe C II C II II

2725

Fe Fe I III

Fe II Fe Fe II II

I

2720

Fe I

2715

Ti II V I II I

2710

Fe Fe I III M I n A II lI I

II M Nn i III I

2695 λ [Å]

M g

2690

Fe II M Mn g II II M g II

M g

2685

Fe I

2680

I

2675

Fe I

2670

Fe FFee II Fe IIII IIII

2665

Fe NI i II I

2660

Fe I FFFNei I ee IIII I I Fe II II

I

2655

Fe I

Fe Fe II II N iI I

2650

I

2645

Fe I

FCe FCeIIII IIII FFe e III I Fe II

χ Flux [erg s−1 cm−2 Å−1 ] 4×10-10

2740

2840

CXIV

2845

I

I

II

I I Fe Fe II FNei III III

Fe I

Fe I

Fe M II n II FFe e Fe IIII II Fe II Fe Fe II M II Fen IIII Fe I Fe I Fe II Sc II II I

M Tin IIII I Fe II M Fen II Fe I I MN II Feni II III M Mn I MF n IIII n Fee III III Fe II Fe II

Fe II M Fen II F I MFee II nIII II Fe II I Fe II M Sc nI II

II Fe II FFNe ei III III M II n I FFe I Fee III IIII N Fei I III

M n

M n

C o Fe II NI i II I M MFen nIII III

M g II

Fe I

MN ni II II

Fe I

FFFeee IIIIII N I iI I M Fen II I I

APPENDIX

4.5×10-10

3.5×10-10

3×10-10

2.5×10-10

5

0

-5

2745

II

II M g

M n

M n

II

I Fe I

M g

iI N

II

I

IIII

II

FFe e II

Fe I

II M n

II FFFee e IIIII II Fe II

M n

II

I

M n II

M n

Fe I

M n Fe II II

I

I

Fe I

II

Fe I

M n

I N

iI

Fe Fe I I Fe II II

Fe II Fe II

CXV

4×10-10


3.5×10-10

3×10-10 2.5×10-10 2×10-10 1.5×10-10 1×10-10 0.5×10-10

χ

5

0

-5 2845

2850

2855

2860

2865

2870

2875

2880

2885

2890

2895 λ [Å]

2900

2905

2910

2915

2920

2925

2930

2935

2940

2945

3045

3050

II Fe I

II Fe I

Fe Fe III II

II C

I Fe I

TFi FeeIII II

I Fe I

Fe Fe I III

I

Fe II I FFee I III

Fe I

I Fe I

I

Fe I

3.4×10-10

F Fe I MFe III enI I III

3.6×10-10

3×10-10 2.8×10-10 2.6×10-10 2.4×10-10 2.2×10-10 2×10-10 1.8×10-10 1.6×10-10

χ

5

0

-5 2945

2950

2955

2960

2965

2970

2975

2980

2985

2990

2995

3000 λ [Å]

3005

3010

3015

3020

3025

3030

3035

3040



3.2×10-10

APPENDIX

CXVI

E. UV spectrum of HD 271791 Comparison of the HST/STIS and HST/COS observations of HD 271791 (black) with a synthetic model spectrum (red) calculated with ADS for the parameters of HD 271791 determined in Chapter 10 and summarized in Table 10.2 and 10.3.


-10

1194 1196 1198 1200 1202 1204 1206 1158

1208

1160

1210

1162

14×10-13

1212

1164 1166

1214 1216

1168 λ [Å]

1218 λ [Å]

1170

1220

1172

1222

1174

1224

1176

1226

1178

1228

1180

1230

1182

1232

1184

1234

1186

1236

1188

1238

1190

1240

I

1156

Fe I

1154

II rI II Fe II I CFe r III M II n Fe III M MgIIII g II

1152

Si I

1150

C

1148

MF ne II I M CFen r II IIII CF r Sei IIIII Si III II M S VFSnei II iI I I I M CSNni I r CFeIIIIII r Fe IIIIII II CS II Srii III III S I Fei II I CFS II MSSreiii IIII n IIIII S C i III rI MC IIII CnII F C e IIII FreIII SSi IIIII C i IIII rI II C rI FS II CMFeeIIII SrnIIIII II I

1146

II

1144

Fe I

C Ci I CFSC Cre IIII SC IIIIII CSS II FreiIIII IIIII Fe C II CFr I reIII III I CMSn Frei I I IIIIII I MFe V MFnIIIIII MFnee IIII FNenIIII IIII CFNe I r I N MFSeIIIII C CFFrnII reeIII CSS IIIIIIIII CVrIIIIII r IIIII II C rI II C Cr Cr IIIII r FeI I I CNi III Fr I CFS eIIIII M FreinI I C CFree IIIIIIIIII C r CSri IIIIIIIII r I F IIIIIII Me III n I CFAN III reliI IIIIII A I l Fe II C III rI I A I lI I

-10

6×10-13

4×10-13

2×10-13

100

5

0

-5

1242

E. UV SPECTRUM OF HD 271791

8×10-13


FFFNee FSeei IIIII S II II C CFSFr IIIIIIII MFFreeieeIIIIIII CFSSSFine IIIIII Freeii IIIIIIIII SFie IIIIII I III CFFe II FVreeIIII FFeIIIIIII eI I FFFNee IIIII FFeei IIIIIII VFee IIIII FFeIIIII eI MF III VFene II VFFeII I FFeeIIII II VFFFee IIIIII eeIIIIIII IIII V FeII M CFn III VFreeIII CFeIIIIIIIII r I CFFeeIII CVFFNreIIIIIIII VSreiIIIIIIII I CViIIIIIIII M rnIIII FSei IIIII III I SCi II V IIII FeIII C FFSFC C CeeieIIIIIII IIIII V MFNi II eI FFFNene IIIIIIII Vei IIIIIIII SFieIIIIIII I V IIII I CFFSe III rei I II VFFFeeIIIIII e AFeIIIIIII VNliIIIII III MV IIII CVFNNeni III M rnII II N IIII FNNeii IIIII F FFee IIIIII FNee IIIIII FF i I VFSee IIIIII V I FFFFeeIIIIIIIIII Neee I I i IIIIII FFSNe IIIIII CFFNSeei IIII reIIIIIII CN r IIIIII VFFFeeIII eIIIIII CFN III C rreiI F FFee IIIIIIII Ne IIIII N i Fei IIIIII III I FFSeei Fe IIII I I I N Ni III i II I SSi M CCi IIIII rn I MCFeIIIII CFnIIII FC CFeeeIIIIIIII C IIIIIII FFFNeeIIII Ne I M i IIIIIIIII n I MSNi III I MNnIIII ni I II MFFee I I MF n IIIII FNene IIIII FFFeei IIIIIIII I Ne III F i IIII CNe III SFNrieiIIII iIIIIII MFe IIII Mn IIII n I MFFe II ne IIII N II iII I Fe Fe III M I n I Fe II Fe I I Fe III C M CFrneIIIII M rnIIIII IIII M Fe I nI I C A Fel I I C III C III A I Sl I SiII I Fe III II MA I n M SMFiel II CFennIIIIIII M rnIIIII III I

CXVII

14×10-13

12×10-13

10×10-13

8×10-13

6×10-13

4×10-13

2×10-13

10 0

5

0

-5

1192

12×10-13

10×10-13


-10

1294 1296 1298 1300 1302 1304 1306 1308

1260

1310

1262

1312

1264

1314

1266

1316

1268 λ [Å] 1270

1318 λ [Å] 1320

1272

1322

1274

1324

1276

1326

1278

1328

1280

1330

1282

1332

1284

1334

1286

1336 1338

1290 1292

II NSi II NS I Feii II IIIII II

1288

Ti I

1258

II

1256

Fe I

1254

C I VN I FeIi II C III III

1252

Fe CTFei IIII Nr III i III SCi II CII I I TFCi I Fee IIIII Fe III NFe III C i IIIII r I V III II I

1250

FFe eI N IIIII I C rI I CN I ri I IIII I C rI II C C CN IIII FFrei II I Fee IIIII I Fe III II I

1248

Si II V I II I Fe C II r C II I rI I CF II Cre I r II III VNi IIII I

1246

N CS i II FSSreii III II C i IIIIII r NIII FNe I C III I

1244

FFe eI TSi III Tii III FeIIIIII I N I I Si I Si III II Fe I FOe I IIIII I SFi eII I NSi I Oi I I N III Sii II O III C I rI II

-10

T NFFieII ei Si IIIIIIIII II I

TF C ei II M FrenI I IIIIIII I TFSeii I IIIII I

χ Flux [erg s−1 cm−2 Å−1 ] 10×10-13

8×10-13

1340

CXVIII

1342

rI

II

TTi Fi III C e IIIII r M IIII Vn I II II MVC I nIII TVFi I I C eIIIII r I FI V e III CV IIII CFrIIII CTFre III M M Crein II FrenIIIIIIIIII I II V II II I

Fe FFe III C e IIII FreI Fe III Fe III C II r Fe III Fe II III I Fe II F Me I n I I Fe II C II I FC Ce I II Fe FCe I III CC II Cr III SC FCieIII I C III I C Mr I Tin II I CF IIIII MreIIII I n M CF II VrenI I IIIIIIIII II

M CFe r CFnIIIII r CFSeeIIIIIII Cr I I r II FFSe III MFCei IIII C Cne IIIII C II CC II I r C F CreIII r IIIII C III Vr I C IIIII r C III rI Si II FSei II Fe III FF III C CFreee IIIII CFFreIIIIIII FreeI II IIIII Fe I I C Cr I r III III M CFF reneII IIII

C

Fe SI CSSii III r II II CSi I I rII V II C III rI II S VI I II I M Mn Fne III IIIII

C Cr r M IIIII Mn I n II III Si I I C I C III rI CSi II r III II

N NI I

APPENDIX

χ 12×10-13

6×10-13

4×10-13

2×10-13

10 0

5

0

-5

10×10-13

8×10-13

6×10-13

4×10-13

2×10-13

100

5

0

-5


-10

1394 1396 1398 1400 1402

10×10-13

1404 1406 1408 1410

1362

1412

1364

1414

1366

1416

1368 λ [Å]

1418 λ [Å]

1370

1420

1372

1422

1374

1424

1376

1426

1378

1428

1380

1430

1382

1432

1384

1434

1386

1436

I

1360

Fe I

1358

iI I Fe I I Si I Si III II I

1356

N

1354

II rI II N FieII III

1352

FFe e II

1350

C

1348

rI II Fe II NFe I Fei III II I

1346

C

1344

Fe S II Fei I I Si II S N i IIII i N III Fei II II NN I iI NFNe II NiiIIII i FeIIII N II iI Fe I NN III NiiI i III II NS SNiii II III I i NFeIIIII i II II Fe I II N I iI N Tii II N Ti IIIIII FeIII I TTi I i III TFei III Fe IIIIII N II iII I TFie N IIII SFiieI I N IIIII iI II

-10

N i F III N e II iI II

NFe FFNeieI I FFFSeeii IIIIIIII Ne IIVIIII i I II II FFe e I F III NFe IIII FFSeei II I FeIIIII Ne IIIII FieI I CFe IIII r II N II FFNei I I ei III Fe III C III rI II N Fei I I Fe III III Si NFF IV ieeII I C IIII rI II


FSei II I

1388

1438

1390

1440

C Fre I I NFFFee IIIII iI FeeIIIIIIII III

Fe Fe II Fe III F III Fe NFSee IIII i I II Fe I N II iI CN Vri II FeIIIII III I

MFe Fn I C M CFre IIIIII SrineIIIIII N IIIIIII FSei i III FeIII I FSei I Fe III I MFFNei II FFne III M CSeine IIIIII rI I CFe IIIII rI FeIIII F SNie III iI I M II CVFFeg II CTFrieIIII FreeIIIIIIII MFSe IIIII FNineiIIIII N IIII Ni I I i Fe II M MFne II n III Fe IIIII I Si I II Fe I SN FeiIIIII FFFe II FSeee I I FeIIIIIII S IIIII N II Fei III Fe II NFe III Fei III IIII FFe II Fee II II Fe IIII II AFFFNee I TileiIIIIII FFe IIII e Fe IIIII N III N Feii II I FFee I Fe IIIII II CFFee I ACr IIII Cl III II I

ASi SSil II iI N III iI I N I Fi I ASei III VFleIIIIII N IIII Sii I Fe IIII Fe III I Fe I FCe III III I Fe II NF I ieI IIII C FFuee I IIII I

FNe i II MFe III Sni IIIII II M I n I NS II ii III I

11×10-13

6×10-13

5×10-13

4×10-13

3×10-13

2×10-13 10

5

0

-5

1442


7×10-13

CXIX

χ 12×10-13

10×10-13

9×10-13

8×10-13

7×10-13

6×10-13

5×10-13

4×10-13

3×10-13

-13 2×1010

5

0

-5

1392

9×10-13

8×10-13


10×10-13

9×10-13

-20 1444

1494 1446

1496 1448

1498 1450

1500 1452

1502 1454

1504 1456

1506 1458

1508

1460

1510

1462

1512

1464

1514

1466

1516

1468 λ [Å]

1518 λ [Å]

1470

1520

8×10-13

7×10-13

6×10-13

5×10-13

4×10-13

3×10-13

2×10-13

1×10-13

200

10

0

-10 1472 1474

1522 1524

1476

1526

1478

1528

FFe Fee II FFee IIIIIII III III Fe FFe I Fee IIII IIIII I Fe FSe II i III Fe II I Fe FSe III I Fe IIII FFN Neei IIIIII i IIIII Fe II II I Fe FFe II Fee IIIIII AII Fel IIII NF III Feei I IIIII FSe IIIII II Fe I II I

FFe Fee IIIII Fe III I CFFe III re II FSeIIII iI FFFFee III Feee IIIIIIIIII III I

-10

ZTFni eI ZTni IIIIII IIII I ZFSNni I ei IIII Si III I Si II TNi iIII FFe IIIII e III III Fe II Ti I TFFei II e IIII I ZSn II Ti I IIII I Fe I FFee I III III Si FSei II III Fe II II FNe I FFei IIII Fee IIIIII II CFFSei IIII re I FFe IIIIII e IIII FFe III FFee I e IIIIIII III FFC Cee I Fe III I I F II ZFne I I I e Fe IIII Fe I II I Fe IIII II I Fe FFe III e III II Fe I II I Fe II I

II FFNe e I Fe III NFe III i III III TFie Fe IIII III I

Fe I


I

1480

1530

1482

1532

1484

1534

1486

1536

C C II C II C II II Zn II F I Tei I I II FNe II N II I

FCe III Zn II I F Fee I FFe IIII Ce IIIII Feo I I Fe III N IIII NFNei II iiI IIII Fe FFe I e III NFe IIIII iI II FFe e I Fe IIII III I C Feo ZFn III e I Fe I III II Si I NFSei I Ci IIIIII M o Feg II FFe III Fee IIIIIII N III iII M I g I Fe I II Fe I Fe II III I M C Feog IIIIII I FNe i III Fe II Fe III II Fe I Fe II SSi III Si I I Sii IIIII I Fe I II I N iI I

ZFFnee II Si IIIIII II I

Fe N II Ti i II II I

N TFei i II IIII II N iI Fe II II

N FieI IIII

FN Neii III IIII I CFNe riI IIII

Fe I

10×10-13

9.5×10-13

9×10-13

1488

1538

1490

1540

CXX

1542

APPENDIX

10.5×10-13

8.5×10-13

8×10-13

7.5×10-13

7×10-13

10

5

0

-5

1492


-10

1594

8×10-13

1596 1598 1600 1602 1604 1606 1558

1608

1560

1610

1562

1612

1564

1614

1566

1616

1568 λ [Å]

1618 λ [Å]

1570

1620

1572

1622

1574

1624

1576

1626

1578

1628

1580

1630

1582

1632

1584

1634

1586

1636

N ZFni I eII N IIII iI II Fe II F C e II Fue II III

1556

FNe iI F I Ne II iI I FFee II IIII I Fe I Fe I I Fe I F N e IIII iII Fe II II FNe i III I

1554

Fe Fe II II N I i FeIII Fe II ZN Nni III i IIII II N II iI II N NFFiee I i Zn IIIIIIIII I Fe II NF II ieI NFe IIII iI N II iI I FNe i NFNei II FieIIII III Fe NF II ei Fe IIIIII II ZNFFni I FFNeeeeiIIIII IIIIIII IIII

1552

S Nc II FieIIII II AFe N l II I Ni I I I NFFei I I ieIII II Fe II NNi III i III Fe II II I

1550

Fe II I FFee IIII

1548

iI I F I ANe II N FeiliII IIII III

1546

N

1544

CNFe ui I Zn IIIIIII FFe II e N IIII I Fei I I IIII I SNci N IIIII iI I

-20

F Sce II Zn IIII II I

CFFe ue II II I I FFe e II Fe III II I


1588

1638

1590

1640

Fe I

Fe I

II

II

II F Fee II II I

Fe I

Fe F I Fee III Fe II III

NF ei I FFFee IIIII Fee IIIII Zn IIIII I Zn III Fe III Fe III II I

C FCFeoo I e IIIIII I Fe I Fe III II

FFe e II III Fe I FFe I e III III Fe I FFee I Fe III IIII Fe I II I Fe Fe I IIII I FFe e III C I FFoe I FFFeee IIIIII e II I III I

Fe Fe III FFe III FFee III e II Fe IIIIII III I FFe Fee II Fe IIIII Fe II I FFe II FCee II C IIIII FFe I I C Ce IIII IIII ZSni FSei II II I I FSei FFSei III I e III III Fe II

FFSe FeeIII Fe IIIIII Fe I I Fe III Fe IIII ZNFFne IIII ei II ZFn IIIIIII eI Fe II II I

Fe II NFFee I I Fei I II Fe IIII III I

Fe Fe I IIII I

9×10-13

4×10-13

3×10-13

2×10-13

1×10-13

10 0

5

0

-5

1642


5×10-13

CXXI

χ 10×10-13

8×10-13

7×10-13

6×10-13

5×10-13

4×10-13

3×10-13

2×10-13

1×10-13

20 0

10

0

-10

1592

7×10-13

6×10-13


7×10-13

-10

1694 1696

1648

1698

1650

1700

1652

1702

1654

1704

1656

1706

1658

1708

1660

1710

1662

1712

1664

1714

1666

1716

1668 λ [Å]

1718 λ [Å]

1670

1720

1672

1722

1674

1724

1676

1726

1678

1728

1680

1730

1682

1732

1684

1734

M g NF II i NFee IIIII Fei IIIIII II Fe II II I N iI I I N N i II iI II F FNee IIII I

3×10-13

2×10-13

1×10-13

10 0

5

0

-5

iI

iI

I

I

I

Fe I

1686

1736

1688

1738

Fe N II FieIII Fe II Fe I I N II Ni I i III II

NFe I FieI I F I C e IIIII u II NFe I iI II

Fe II N i Fe III II I Fe II

I

Fe I

N iI I Zn I Fe III II Fe Fe II Fe II II F I FFFee I ee IIIII IIII

II FFAel e III I

Fe I

Fe I

N iI NFe III i I II II

N

I

II Fe I

N

F NFee I i IIII N II Fei I III Zn II I N NF i I FFFeeieIIII e IIIIII FFFee III e IIIII I Fe N II FCei III Fe I I FCe IIII FCe IIII I C C II I Fe NF II ieI IIII

I Fe Fe II II

1646

Fe FFee II IIII I N iI II N iI N II iI I N I Ni I Fei IIII II FFee II IIII I Fe I N II Mi II Nn I Fei IIII III I

4×10-13

Fe I

5×10-13

1644

N iI II C Noi CN iI CFreIIIIIII o III NFF III C eieIIII u IIII FN II NFeei I I Fei I I Fe III I FSei IIII I CNFSei III ri I I IIII Fe I Fe II III N iI F I Ne III i I N III iI N II CFi I oe II I N IIII i Fe III II I N NFieII i NF IIIIII ieI NAl IIII i CNi IIIII r II I NFFCeIIII i I NACe IIIIIIII il I I C IIII NII CNCii II u IIII NF III ei I I I F I CNFei II o e IIIIII N Ni I IIII FFAieIIII el II I I


6×10-13

Fe II Fe Zn I IIII I

-10

C NFoe I i IIII III F Ne i III I C I rI I N I CNi II ri I FeIII I CNi I o II II NN II FieiIIII III NF Siei IIII III

NFe Fi IIII N e III Fi I Fee III I NFe III CNi II oi I I CFFe II reIII IIII

χ 7×10-13

1690

1740

CXXII

1742

APPENDIX

χ

8×10-13

1692

7.5×10-13

6.5×10-13

6×10-13

5.5×10-13

5×10-13

4.5×10-13

4×10-13

3.5×10-13

3×10-13 10

5

0

-5


-10

1794

7×10-13

1796 1798 1800 1802 1804 1806 1808 1810 1812 1814 1816 1818 1820 1822 1824

1774

6.5×10-13

1826

1776

1828

1778

1830

1780 1782

1832 1834

1784

1836

1786

1838

iI II FFe e III III S Fei III NFFe III ei F III Fee IIII Fe III Fe IIII III I

1772 1788

1840

1790

5×10-13

4.5×10-13

3.5×10-13 4×10-13

2.5×10-13 3×10-13

2×10-13 10

5

0

-5

1842 1844


λ [Å]

1770

N

1768 λ [Å]

I

1766

Fe I NF II ei III III Fe II N iI FFe II e III Fe III Fe II III I

1764

iI

1762

N

1760

iI II Fe II CNi I o F IIII Ne I II FieIIIII II

1758

N

1756

N NFFei FFeei IIIIIII Fee IIIII IIIII Si I NFSei II i III II Fe II NF Feei IIII IIII Fe I N III iI I FFe Fee III I IIII N I iI II S I Fe I N II iI I II FFe e II III I

1754

iI II FSei IIII I NF ieII III N iI II NF FNeei I i IIIIII NF III ei III II Fe I II I

1752

N

1750

Fe S III I N I iI I FSe II I

1748

II

1746

N Fei I IIII I

1744

N iI

-10

NFe i III II

F Fee II II I N iI II


N i N II CF i I I Noe III F i I II Ce III o II N III iI II

FFe Ne IIIII NFei II I iII I N I Fei I IIII Fe I II I N iI N II i C III o II I N Ni I i II III Fe CNi III oI N IIII iII I Fe N II FieIIII Fe II II CNFie I o III III I F Ne I NNi I I ii C IIIIIII o II I

N Ci I NFo III Feei IIIIII IIII I N iI FFe II e III Fe III F II C e II NFoe I I Ni I II i III I

NAl I iII II

CFACl I Noe I I Ci IIIIII II Fe I A II l N II iI II N Ai I l Fe IIII N II iI II A lI I

iI II C NF II ei II III I

N

NNi i II III

II F NFee II Fei IIII N IIII i I FNe III Fei I III Fe IIII Fe II III I Fe II Fe I II N I i N II iI N II NF i III ei I IIII I

Fe I

N Fei II III I

7×10-13

CXXIII

7.5×10-13

6.5×10-13

6×10-13

5.5×10-13

5×10-13

4.5×10-13

4×10-13

3.5×10-13

3×10-13 10

5

0

-5

1792

6×10-13

5.5×10-13


-10 1945

1950 1855

1955 1860

1960 1865

1965 1870

5×10-13

1970 1875

1975

1880

1980

1885

1985

1890

1990

1895 λ [Å]

1995 λ [Å]

F CFFee I uI Fee IIIIIIII F I FFee IIIII Fee III Fe IIIII Fe IIII NI Fei III FFe I I Fee IIIII IIIII FFee I Fe IIII III I FFFee I FFee IIIIII Fee IIIII Fe III II FFe I Fee III II Fe III FFee I IIIIII Fe I NI i III I FNe i M IIII n Fe III II I FFe Fee III IIIII M I n II FNei I IIII I M n I Fe II I MFFe II Fen III CFe IIIIIIII u CFe I MCFFFreeueIIIIIIII I Fen IIIIIIIII MFee IIIIIIII CFen IIII FFFre I IIII ee IIII II Fe III FCe III FFeu I e IIIIIII III

1850

II FFe Fee II Fe IIIIII Fe I I IIII F I NFe I i Fee IIIIIII FFe I I FFee IIIII e IIIII Fe IIII Fe II FFe I I e IIIII III Fe AI l III I FFFee I e II FFee IIIIIII I Fe IIII FFee III Fee IIII Fe IIIIII III I

-10 1845

Fe I

FFe eI F IIII Me III FFen I Te III MFi IIIIIIII Feen I Fe IIIIIII FFe IIII eI I MNFen IIIII FFNeei IIIIIII FFeei I II CFFe IIIIIIIIII oee III F III Me IIII NFFn II i Feee IIIIIII F III CFFee III Foee IIIIIII FFFe IIII Feee III I FFe IIIIIIII MFFee IIIII Feen III NFe IIIIII FNei IIIIII Fei IIIIII Fe II FFe III eI I Fe IIIII I C II o II I FFe e III III

χ Flux [erg s−1 cm−2 Å−1 ] 5.5×10-13

5×10-13

4.5×10-13

1900

2000

1905

2005

1910

2010

1915

2015

1920

2020

1925

2025

1930

2030

1935

2035

1940

2040

CXXIV

2045

FFe FFee IIII e II Fe IIIII FFe I Fee IIIII M FFe IIIIII FeenII Fe IIIIII FFe I I FFee III FFe IIIII CFeee IIIIIIIII Foe IIII Fe IIII FFe I I M FFeenIIIII II FFee IIIIII e I FFe IIIIII Fee III Fe IIIII FFFe I I Feee III Fe IIIIIIII Fe III I CFFFFee IIIII oe II CFFFeee IIIIIIII o NFFeee IIIIIII FFACeilIIIIIIIII e III I F III MFee I n III IIII I AFe Fl I M CFFFeenIIIII Foeee IIIII Fe IIIIIIIIII FFe III eI I CFe IIIII Fo MCe IIII Feno II III MF III en II M IIII n II I

AFAel I Fel IIIIII I FFe III FFee III II FFee IIIII e IIII III Si FSi III FSSeei III FFei IIII II Fe IIIIIII eI I Fe II II I Fe II Fe I FFee III Fe I I IIII I Fe FFFNee I I FFeei IIIIIIIII e III FFFFeee IIIIII II Fee IIIIIIII Fe I I FNe IIII I FFFeei IIIIII FFee IIII I I Fe IIIIII FFee IIII e III FFFe III FFee III FFSee IIIIII FFeei I IIII Feee IIIIII III FFFee IIIIII FFee IIIIII FFee IIIII FFee IIIIIII FFee IIII I Fee IIIIIIII II FFee III Fe IIII Fe III FFe I I I Fe III NFFee IIIII Feei IIIII FFe IIIIII Fee IIII IIIII I Fe II FFe I II e I FFe IIII e II I III I

FFe eI F IIIII NFeie II Fe IIIIII FI N NFFFeie IIII FFeeei IIIII II Fee IIIIIII II Fe II MI n NF IIII AFFei I Feeel IIIIIIIII A IIIII Fel IIIII I A II NFFel II i III e FFFee IIIII e IIIII III

APPENDIX

χ 6×10-13

4×10-13

3.5×10-13

3×10-13

2.5×10-13

2×10-13 10

5

0

-5

1945

4.5×10-13

4×10-13

3.5×10-13

3×10-13

2.5×10-13

-13 2×1010

5

0

-5


-10 2145

2150

4.2×10-13

2155 2160 2165 2170

4×10-13

3.8×10-13

3.6×10-13

3.4×10-13

3.2×10-13

3×10-13

2.8×10-13

2.6×10-13 10

5

0

-5

2185

2180 I

2175 iI

2190 2195 λ [Å] 2200

iI I rI II

2205 2210 2215 2220 2225 2230 2235

rI

rI

II

II

II

2135 2140

2240

CN ui C II rI II

C

rI

2130

C

2125

C

2120

II

2115

rI

2110

C

2105

N iI I C u II MFNe I FNneii IIII I N II I Ni I Fei II N III Ni I i II I CNi Mr IIII n I II I

2100

N i N II iI I Fe I CFNe III u Ni III iI I N Fei I III

C

II

2095 λ [Å]

N

2090

rI

2085

C

2080

CN CriII Nr III CN uii I I III

2075

N

2070

CNi Nr III i III I

2065

FNe FNeii IIIIII III N Ni i III I CN ui I N FNei I i IIIII II

2060

N C iI Fre III III I N i N II i C I Fre I I IIII I

2055

FNe Fei IIIII II

2050

Fe FNe II i IIII II

Fe I Fe II I C CFr II re II C IIIIIII rI II Fe Fe II C III rI II

-10 2045


2245


N FNei I I CF i IIIII eu I Fe IIII II CNi I r III II C rI II F CFFee II re IIII III

N iI I

I III N I i CN II ui N II iI I N iI I

C Feu

F MFe I Feen IIIII IIIII I Fe F Fee II Fe IIIII Fe I I M MFNen IIIII eni I Fe IIIIIIIIII II Fe I FNe I i IIIII M II Fen Fe III Fe IIIII NII MFFeei III n IIIIII Fe IIII M I C n II MFre III n IIII IIII I C FFre I e IIII C IIII Cr I r II C III CFre II Nr I I FeiIIIII II I Fe C II u I CFNi I Cre II r C IIII r III I Fe I C III C r Fre IIII IIII I

M n I Fe II I Fe II N II iI I

M Fen FFe IIIIII eI C IIIII rI I M I MFen I n IIII FFe IIII e II Fe III I Fe II F I CFe III u FF e IIIII MFee IIII en IIIII FFe IIII FSee II FSei IIII Fei IIIII III I FFe e II III I Fe II Fe Fe II FFe II Me IIIII n I I Fe II II Si I Si II II

CXXV

χ 4.5×10-13

4×10-13

3.5×10-13

3×10-13

2.5×10-13

-13 2×1010

5

0

-5

2145

4.4×10-13

Flux [erg s−1 cm−2 Å−1 ] 3.5×10-13

-10 2345

2350 2355 2360 2365 2370 2375 2380 2385 2390 2395 λ [Å] 2400 2405 2410

2315

2415

2320

2420

2325

2425

2330

2430

2335

2435

FNei I Fe IIII Fe II II

2310

Fe Fe II Fe II Fe II II Fe Fe I III FFe e II II

2305

Fe Fe I FFe III e III I

2300

Fe Fe I III F Tie II FeIII N II iI I Fe Fe II II I

2295 λ [Å]

Fe Fe I III Fe II

2290

Fe FFe II e III I

2285

N N FFeii III e III II

2280

I

2275

iI

2270

N

2265

N i CFFee III o III II

2260

C Foe II I Fe I I Fe I I CFFee II o II Fe III II

2255

Fe TFi II NeI i III I

2250

Fe FFe I Fee III IIII Fe II C o Fe II II FNei N II iI Fe I II Fe II

I C o I FFFee II e III N II iI I

-10 2245

Fe I

FNei I Ti I I FFe II e II II


3×10-13

2.5×10-13

2340

2440

CXXVI

2445

I

I

iI

rI

II

FFee III Fe II II N iI I N iI Fe I V TFei II IIII F II FNee I i IIII I FN Feei I I II

rI I N I i Fe II II

C

CNi rI N III i II I

C No II Ni I I i C II CCo I roI I I N III iI I

CN Noi II iI I

N Ni I Ni III iI N I iI I

CN i N NiIIIIII i N Ni III i III N I Ni I i II I

C

C o N II Ni I i II I

N i N II CNi I riI I N II iI N Ni I I i I Fe II II

N

Fe I

CFNei r III II

CN ui IIII Fe II C Cr I r III Fe II NI i II I FNe i III C I Cr I r III II Fe II C r II I

APPENDIX

χ 3.5×10-13

2×10-13

1.5×10-13

1×10-13

0.5×10-13

10 0

5

0

-5

2345

3×10-13

2.5×10-13

2×10-13

1.5×10-13

1×10-13

0.5×10-13

10 0

5

0

-5


3×10-13

-10 2545

2550

2.5×10-13

2×10-13

1.5×10-13

1×10-13

0.5×10-13

10 0

5

0

-5 2455 2460

2555 2560 2565 2570 2575 2580 2585

I

I

2590 2595 λ [Å] 2600 2605 2610

I

Fe I

2615 2620

2525

2625

Fe I Fe I Fe I FFe III Fee I IIII I

2520

I

2515

Fe I

2510

Fe Fe II II

I

I

2505

Fe I

2500

Fe I

2495 λ [Å]

M n I Fe I II

2490

Fe Fe II II

2485

Fe I F I Me II n II

Fe I

2480

Fe I

I

2475

Fe I

2470

Fe II M Fen I I Fe II II

I

2465

Fe I

Fe TFi II eII I Ti II F I Tie I III I

I

2450

Fe I

FFe Fee II III I

FFe Ne IIII iI I

-10 2445

2530

2630

2540 2545

2635 2640 2645


2535


I

Fe Fe II II Fe II Fe FFe I e II Ti II FFeII I SFie IIII eII I Fe II

Fe FFe II Fe III Tie III II I Fe Fe I III

Fe II Ti FeIII II Fe II Fe FFe II Fee IIII II

II N FCei II IIII

C

I Fe II Fe FFe II Fee I IIII I Fe II

Fe I

FFe eI Fe III Fe II II Fe II

Fe II Fe II F CFee II r III Fe II II Fe II

FFe e III I Fe FNei II III Fe I II

Fe Fe I II Fe I Fe II FFe II Fee IIII F II eI I

Fe I

Fe FFe II FFee I II Fee IIIII Fe I III

CXXVII

3.2×10-13

3×10-13

2.8×10-13

2.6×10-13

2.4×10-13

2.2×10-13

10

5

0

-5


I

I

I

Fe I

Fe I

Fe I

I Fe I

I Fe I

I

I

Fe I

I

Fe I

Fe I

Fe I

I

I

Fe I

Fe I

I

I

Fe I

Fe I

I

2.5×10-13 2.4×10-13

APPENDIX

2.6×10-13

2.3×10-13

2.2×10-13 2.1×10-13 2×10-13 10

χ

5 0

-5 2715

2810

2815

A

2730

2735

2825

2830

2835

I

2725

II V

lI

I

2720

2740

2745

2840

2845

C C II II

2710

M g

M g

2705

II

2700

II M g II

2695 λ [Å]

II

2690

M g

2775

2685

I

2770

2680

Fe I

2765

2675

I

2760

2670

Fe I

2665

I

I

2660

Fe I

I

Fe I

2655

Fe I

2650

Fe Fe I III FFe e III I

-10 2645


2×10-13

1.5×10-13

1×10-13

0.5×10-13

10 0

χ

5 0

-10 2745

2750

2755

2780

2785

2790

2795 λ [Å]

2800

2805

2820

CXXVIII

-5

II M g

M g

II

CXXIX

2.2×10-13


2×10-13 1.8×10-13 1.6×10-13

1.4×10-13 1.2×10-13 1×10-13

0.8×10-13 0.6×10-13 0.4×10-13 4

χ

2 0 -2 -4

2845

2850

2855

2950

2955

2860

2865

2870

2875

2880

2885

2890

2895 λ [Å]

2900

2905

2910

2915

2920

2925

2930

2935

2940

2945

3045

3050

1.95×10-13

I Fe I

1.85×10-13 1.8×10-13 1.75×10-13 1.7×10-13 1.65×10-13 1.6×10-13 1.55×10-13 4

χ

2 0 -2 -4

2945

2960

2965

2970

2975

2980

2985

2990

2995

3000 λ [Å]

3005

3010

3015

3020

3025

3030

3035

3040



1.9×10-13

APPENDIX

1.85×10-13


1.8×10-13 1.75×10-13 1.7×10-13 1.65×10-13 1.6×10-13 1.55×10-13 1.5×10-13 1.45×10-13 4

χ

2 0 -2 -4

3050

3055

3060

3065

3070

3075

3080

3085

3090

3095

3100

3105

3110

3115

λ [Å]

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Acknowledgements I would like to thank my supervisors Uli Heber and Norbert Przybilla. I am very grateful for the opportunity to investigate this fascinating scientific topic. Moreover, I would like to thank for the chance to follow my own science and for not putting any pressure, but letting me influencing the direction of this thesis and pursuing my own research. Also I am very grateful for the always open door and the discussions. I would like to thank for giving me the opportunity to broaden my observing experience. Furthermore, I am thankful for the chance of participating in a large number of international conferences. Thereby I would like to thank Australian National University for support to participate in the Nuclei in the Cosmos summer school. I am also grateful for the opportunity to move to the beautiful Innsbruck during my thesis. I am thanking the University of Innsbruck for providing me with the facilities necessary to finish my thesis. Furthermore, I would like to thank Stephan Geier for the long discussions and the great support and for the opportunity to be a part of the MUCHFUSS project. and for encouraging me to start my own project. I am also grateful for his invitation to stay at ESO for one week, which was a great experience. I am thanking also Thomas Kupfer for his contribution by getting observing time essential for this thesis. Moreover, I am grateful to Oliver Cordes for sharing his observation time with us. Many thanks also to our Bachelor students Ingrid Barbu-Barna and Kathrin Nagel for their contributions to this work. I want to thank my colleges at the Remeis observatory and my colleges at the Institute for Astro-and Particle Physics for the great working environment, which not only consisted of work. Especially, I want to thank my office mate Andreas Irrgang for his help introducing me to the subject of abundance studies, his help with ISIS and the discussions. I am, moreover, grateful for the open door, support and many discussions with Horst Drechsel. I also want to thank Joe Schafer for his helping hand on whatever computer problem and Silvia ¨ Ottl, Miguel Urbaneja, Felix Niederwanger and Fernanda Nieva for listening to my problems. I also would like to thank the subdwarf community for the great time at several meetings and the many collaborations that resulted from them. Especially I want to thank Brad Barlow for giving me to take the lead on our project and also sharing with me the lead in our future big project. I also want to thank Dave Kilkenny, Pierre Maxted, Roy Østensen for the collaboration. Moreover, I am grateful to ESO and Calar Alto for granting us observing time, for the staff in the great support during the observations and for ESO and DFG for the travel grants. This work is supported by the Deutsches Zentrum f¨ ur Luft- und Raumfahrt (grant 50 OR 1110) and by the Erika-Giehrl-Stiftung. Furthermore, I would like to thank my parents and my husband for their support and understanding in this stressful time, especially at the end while finishing the thesis. And I am grateful to Guy Burns to agreeing to proofread this very long thesis.

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